Trigonometric Ratio & Identities FULL CHAPTER | Class 11th Maths | Arjuna JEE

0:00 This question asked by Ji Maa is an interesting thing that in 2019 it came in 2022 Exactly similar question in advance I had asked about similar fund giving 9x on top Cons will read their graphs which are NCERT so these six things are those which For NCERT as well as for GK It is important, it will work for both rhythms Streets or your brother NCERT Kari R Di Sharma pick up any book and You are putting 10-10 on the same formula You are asking questions and slowly You have learned the formula, we have done this We have first divided the lecture face wise. do all set of formulas which only were in NCERT and I read all of them If you have made this application also then Individually understand each chapter conceptually If you have read it in depth then you will know The questions become more difficult as they reach the end you will not look Hello children how are you son

0:46 how are you guys you all are great You are happy, having fun, enjoying life You have come, it is good son, let's go then I will tell you all I welcome this Arjun son My name on youtube channel is Tarun Khandelwal Many of you kids probably know me You may know, maybe you don't, even if you don't know, For this I will introduce myself by my name Look, it is written in front that Arun Sir is right I will take your maths from the lecturers ahead of you In which we son give one shot to each chapter I will do it and a little bit in my big one Maybe you don't know, so I did it myself My son has completed B.Tech from I.D. Delhi My rank was 289 in IIT and For many years I have been looking for kids like you The important thing is that I am helping them Help them prepare to clear this

1:31 I am preparing for competitive exams, son Look at this batch of kids, this is what happened in my elder now in this match of you A lot of kids must have come, so look at this batch I will talk about two kinds of children One for those who have read this chapter It hasn't been lying around at all trigonometry ratio trigonometry Identity means trigonometry one also like They say we are right, we will read it one Create a backdrop inside the shot If it has happened then this is for them that brother you You can clear your backlog by this in concept we will do it in this and Other people who want to do a revision, quick revision want to do it brother have read it and maybe I have forgotten or I don't remember it that well If it is there then those people should also see its revision and in between ask questions to yourself You can try right and those who have I have also done the revision, that is just the questions Do it from the middle, everyone has to see whatever

2:18 There are kids in 11th, I have to see everyone, son There will be something for everyone in it and I received the lecture very well I have planned it for you guys, note these What is there in the terms of bus, there is nothing like that you will get everything proper first i I will get you the basics done, whatever you want There is basic stuff in NCERT, I will get you to do it one by one I will do all the NCERT together so that You can also prepare for school exams How far are you from NCERT? Do you know about it? I want it friend, till here there is NCERT and now this The thing is outside NCERT i.e. only This is going to be the level right so like this We will plan our lectures from everyone For kids You will definitely get something and I hope you enjoy this lecture Son, I am very excited for you Sharing this Youtube journey with people Continuing, Arjun started the batch

3:04 Son, turn your first chapter towards me from which you guys are going to get this Trigonometry Ratio and Identity Let's do it get ready let's start let's start Son, this is a recording session, see, this is a purpose It is to give a recorded session and not to take it live because a lot of kids might have There is a backlog, some have half, some have 14th someone's just like I told you different Children can listen to this lecture in different ways I have to take this lecture, I have to consume it It may be right that you have read the entire chapter If you haven't read all these topics then you will lose all eight okay, we will read it today from the topic Trigonometry Ration and in English In identity and whom you take as your mother, this is basic come on friend what is this light angle what is a negative angle what is a What are compound angles with a + b what are double triple they are straight Jump to the questions directly to the level

3:51 even on things that you can do it right so that's why recording I have given you a session, so let's start What is today's goal? Today's target What is it as I have shown We will do eight things for you first Introduction Introduction means basic key Brother, in this chapter, will we discuss Trigonometry? Where do I start this chapter from? After that, don't see it in this chapter So friend, there is only one thing, formulas are okay Formulas Formulas Formulas Just as much as you Learn the formulas of the chapter well The more people you are, the happier your son will be Chances of getting questions from you increase I will go okay, I have seen many children that how they do it hey sir learn what Sir there are 50-60 formulas, who are so many? you will learn sir, I will do one thing with the notebook I am lying down in front of you and everything is written there, Sir And after seeing this I will ask a question Sir

4:38 If he is here I will look at him like this Sir, you will learn gradually Son, you have no more wrong strategy than this ho shakti yehi point of view se thal ke tal This strategy of yours will work brother NCERT Kari R D Sharma pick up any book You are using the same formula and You are asking 10-10 questions on me and Slowly and gradually you learned formula is ok that can be in butt What is a son? Such questions do not arise that I will see straight away this is the formula You have to apply this son, come on apply it and get the answer It does not happen that I give you the thought process you have to develop, you have to understand friend which formula will you use now You don't know of any such formula If it even exists then how will you find it you have kept a notebook front now i ask you sign square a minus sine square is also the formula of

5:23 You don't know it because you You will search in your notebook which one it is but this is it If you asked a question in it, then why not How do you get the questions in it? Just memorizing the formula is not important It should also be remembered that the formula What all things do we have Understand that he is asking you a question based on a formula We will not give tax if there is mixing in place You have to find out for yourself which one when will you be able to find the formula when you One By One Formula One By One Formula By Heart The son has learned it, so whatever children this watching the video for the first time which is the second time You can see who is studying me in Arjun batch They are ready and they know this that sir you have spoken about triangle Learn the formulas very well if you guys are doing this for the first time are you looking at one shots so today when you see After that, I will tell him whatever formulas I can

6:10 You can write a short story in a different place in a proper manner Write down notes and learn them again and again Now you should learn them well You will say sir you are not learning what to do What if you can't learn the track formulas? It's a wonder brother, I am not learning from you The whole world does this whoever comes in 11th hey maths is late everybody does it, we have to think like this Do not think that this is not being learned It is very easy to say there are 50 formulas sir how you will learn sir then all the kids do it and boards Let's clear it too, friend Commerce students also do it that brother you guys can do it why can't you You can do it friend, when others can do it then you can do it too If you can then no one will say anything to this sister sir I am not able to learn, promise me you will do everything People write on chat and yes sir we have formula I will learn well and I will learn like this

6:56 No, I am not talking about such a formula learn this is not good sir sign you are very good yes yes sir i am remembering something it is good sir suit tu sign tita kas tita nahi sir mines you are so bitter not like this Proper learning means learning from the very beginning you should take it out from your mouth right then it should be like this I would give the kids an example. I wonder how can I remember someone's name from you Ask yourself, your name will come out correct or not yes brother my name is rohit sharma sir Our name is Virat Kohli even in our sleep If he asks, will you tell me the correct name? Is it true that someone can suddenly wake up from sleep If you ask me brother what is your name then I will sleep Even if it happens, the correct answer will come out the next day You don't even remember that you told me someone I had asked his name while sleeping at night Formulas must be learned

7:42 what happened the situation got worse but what did he say you gave You will have to do trigonometry formulas It won't work without it and one more thing I had said this in Archana batch which you guys I will repeat this for all the children Look son, there are two types of kids in 11th standard There are some who take care of their mother silently and learn all the formulas ok the teacher has said it, sir has said it I have told you in school too, I know, I understood those who were going to turn on their importance I was also singing, I did it and others are like that It is from those who are the first and foremost sons There is a lot of roti and after that I get very upset They do a lot of drama that Sir, we don't know What should I do if it is not happening then If you want to go and learn, son, you should learn because they know the boards too

8:29 You will not be able to clear 12th if you do Trigonometry You did not learn the formulas till rate 12 If it comes in less quantity then its your choice Which category do you want to be in? Learn silently in the first category Did it without drama or in another category Sir, we will keep it first and then wash it we will go and learn okay so let's go to this Sir let's start with the introduction now You have created such a fearful atmosphere I have created so many formulas, look at them don't be afraid here is the truth i will show you you are lying, hey it is a very easy thing You may think that I will read it and go away My backlog has been cleared and you brother Your tension is roaming free, don't do that I need to tell you the right thing, son. The thing is, there are a lot of formulas in it. You will have difficulty in learning but you everything that has to be done will be done, you too do it Now what will I do for your ease

9:15 because the 5060 formula is based on such thinking Thinking about it I felt that a messy match had happened so I Made a separate set for each formula A formula called Allied Angle has been created diya what is negative angle by name only You must be understanding that its set is different compound angle A plus B A minus B ones right O ones Double angle sine tu tita cos2θ Triple angle Three-Titan Factorization Factorization I am telling this for those who have some idea. hmm sun c plus sign di etc you probably If you would have seen it I I am zooming in a little bit Have you seen the story yet? I must have taken it in 11th, it was August In two-three months, people read the story and some You may have seen some triangles but you also did not see them Never mind, this is the first formula We will use five of them, all of which are in NCERT as well. After that a light graph became soft trigonometry functions finex cusp x

10:00 We will read their graphs which are in NCERT If yes then these six things are those which are given by NCERT It is important for me and K as well After this both have numbers together see what is written This is the extra formula we are for Pacific Re offers a variety of formulas and After that if we start then this is the same topic There are not many different formulas in it will come for the problem above We will practice, Piyush will also practice And lastly Range of Trigonometry function so last key two with eight number you this Understand that this is just for you It is important for the first six boards as well KK Sorry is important for school also And it is okay for K too brother, let's go now We begin with this first We will study radium in the introduction it happens son because you must have heard the word Sometimes we get confused with radium

10:47 Like we have to write decrees till today we are in a hurry You used to take the unit of degree, right? If it is placed on top of the forest like this then this forest degree becomes right like this now a new What is its reduction on unit added radium At least we have got a good degree Son, what is the difference between me and kilometer and two units? tell me how do I measure distance We also measure time in kilometers and minutes. I also do it in seconds so she is like this units have different meanings between them There will be a relation because any two units There is a relation in between, right brother? Yes Sir 100 kg is 100 grams equal to 1 kg It is like the same thing, your degree And radium will also work in this degree In a way, radium is like this If I want to write then I will write forest, only forest If you have not applied anything on top then you can add that

11:33 Is it radium or should we put it on the forest like this this also represents radium okay so if mother i have written year 30 degrees and I will put 30 over 30 like this It is a degree but it is written year 30 Understand what this is, son, this is radium What is radium now as I said There is a relationship between the two units If you want then there is relation P radium equal to 180 degrees The value of m radians and 180 degrees is equal 3.14 whose value is approximately or 22/7 of that If we call approximate value then That much radius = 180° why sir

12:19 It happens But why are there only 60 seconds in a minute? why aren't they 50 brother because Any one unit has been defined defined in other unit terms such as It has been done, it will remain the same, son Your questioning won't help him There is no proof that fire radium is like this is defined as 180 degrees If there is fire radium then should I write 180° equal to Okay so obviously by the unitary method what will happen if you do it on both sides then what will be the radium of π/2 at 90 degrees Will be done Sometimes I'll write 90 degrees or π/2 I will tell you the same thing, year 10th class of 1990 since you are studying it becomes one, right, from now on We will also see the story of Sun π/2 written on it One said we will do it, okay brother, do it half more take bye bye four it will be 45 degrees okay

13:07 yes sir now you understand that it is kept at 180 So it changes in degrees, right? If I ask you how much will bye-bye3 be put p to 180 so 180 / 3 is 60 degrees will What will be π/6 180/6 will become 30° What will be π/12 and divide it in half to get 15 it will be degrees and so on 1 degree how much Will be done it will be π/180 sir okay this way you Degrees to Radium to Degrees to Radium I can turn it around which is your mother you can do it right why do you want to do it sir Son, see what happens in higher classes. I used to tell you in the lower classes sign 45 degrees now that's a little bigger flower If you tell me to do π/4 then I will Sun π/4 and 45 are the same thing right π/4 and 45 It is the same thing so this is 1/√2 10th

13:54 class ki trigo brother dekho needles tu se Meaning there is no need to eat honey that is 10th I should know trigonometry at least Look brother the regular Arjun was the best there I also revised Hockey Fulki for 10th but friend we can do 11th in one shot Now I have to do it, I will do it for 10th also, then So it's done, you should know 10th class trigo You all have cleared 10th, son. that whatever Trigo was, it will come to you should be ok So let's talk about degrees and radium The degree of major and the relation in radium now Is there another thing that is really cute what happens son, what happens is that you don't get a degree There is also a smaller unit in This is the change in degrees into radium Now it happens many times like mother

14:41 7 or let's write it as 7.5 degrees what can you do, 7 degrees are enough the whole and the part with points Further we can change it to even smaller unit Let us take the value of one degree It is 60 minutes but what is this? degrees and minutes like there are 60 minutes in an hour So it doesn't say that there are 60 minutes in an hour Why is it so, think about it for a minute. We have also calculated the unit of angle in degrees. Defined that 1° = 60 minutes and shortened it To remove the define decimal as we need We don't say it like this many times, right? 1.5 Hours one over gives 30 minutes same as

15:28 some have 1.5 degrees what is 7.5 degrees will say 7 degrees and 60 in one degree If it is then how much time is there in 0.5° then it is 30 minutes 7 degrees 30 minutes we will write it like this Should I write 7.5 degrees or 7 degrees 30 minutes If I write it is okay then the degree should be a This is how we fractionalized the degrees in fractions a little bit then in 1 degree 60 minutes came just like it happens in the voice, friend It feels strange to say 1.75 overs, right? 1.55 Ours so we did it to resize it Why did the minutes and seconds come like this? Think about why there are minutes and seconds in time. It was already an hour, brother, we came according to the hour I give you the answer but the precision doesn't come Someone tell you friend it took me 1.375 overs

16:15 Youtube to attend this class from here of Are you crazy man what is this 1.375 to me So I don't understand, one hour or a few minutes If it takes so many seconds you will understand yes friend I understood what he said and then What is the use of giving up seconds? accuracy flooded accuracy because we You know we are very careful about time There are too many emotions sir time we measure very accurately and they waste a lot too isn't it okay let's do jokes in apart time like that Son, even the measurement of degrees is very important to us. need more pressies You can't tell us like that friend 12:30 degrees A because 22.5 6 7 8 if the degree became something like this then why why do you need search now you will say why You should think about it, someone should study the planets

17:01 is 22 degrees or 22.5 7 8 decimals will make a difference Chandrayaan has gone, you all know now If yes then how much calculation will be required Scientists have done it in the way you are thinking He rounded one to the eight decimal place you must have taken it out and left it, not those angles People changed it into their son and it too would we have left even one degree not even one degree we are 60 I will agree after a few minutes and now you you must have understood and further you must have understood that a And the unit of time is like one hour in 60 minutes and in a minute there are 60 seconds something like that Son, the same thing happens to some degree. 1 degree in 60 minutes and 1 minute in Further 60 seconds will pass and what is there to fear

17:48 60 seconds will be enough if you understand The angle has become more precious, you think how I will write to you mother, someone wants to tell you that brother a reduced tax 7.55 degrees, you just wrote anything like that, 7.55 Convert degrees to degrees minutes and seconds tell me what will you do 7th degree yes sir now it is in point five five degree Find out how many minutes it is using the unitary method Look people, there are 60 minutes in 1 degree. There are 60 minutes in a degree so our number is 0.555 pass 5 5 how many will be in it 5 5 * 60 calculate brother how much will it be This is 5.5 points

18:35 * 6 is it brother take it out quickly 5.5 * 6 I wrote anything like this friend 5.5 * 6 33.3 So it's been 33.3 minutes, then someone will say yaar I don't like these minutes in decimal is it not so 7 degrees 33 minutes and which It's point three minutes, take it away son then change it to seconds because one minute In 60 seconds one slave means in minute two slaves I mean second, you must have understood this no 0.3 now what do we have to figure out 0.3 How much is the part in this because it has become 60° And it's 33 minutes in and this is 0.3 which is how many will be there in 0.3 minutes

19:23 60 * 3 It will be seconds son, see how many have passed It will take about 18-18 seconds sir, so actually this instead of writing this thing 7.5 degrees we what will you write 7 degree minute and 18 seconds like this What is happening? Accuracy is increasing. The accuracy of the angle which was in decimal We have degrees and minutes degrees minutes Just think about the calculation done in seconds, 7 hours Like 7 hours 33 minutes in our time minute 18 sec that it is better to say It is a relief, I can say that 7.5 overs are butter than that Degree is absolutely everything in degree Who used to be mine, would have been mine, son

20:11 Let's go right within the time so now a small I will give you a quick question on this can you pose with it and take it out what are you saying this is the degree notation it is written in change degree to degree only The degree has to be kept in radium I don't want to take this degree in just one way If it is a fraction part then what are you doing now change this to a fraction degrees yes but after removing minutes and seconds it will become a fraction I can bring it here, how can you see it is 45° I only have 15 minutes and 30 seconds left now Look how many minutes are there in 30 seconds 5 minutes are 30 seconds equal to two points five minutes okay so firstly I gave it to you How did you write 45 degrees and it was 15 degrees

20:57 were to him 15 minutes and 30 seconds is divided by point five to 15 It's point 5, son. 5 is also 15.5. minute so basically now i'm growing up What was the focus of the unit previous question Look from last minute to last minute It had to be changed in a second, it is the opposite If you want to convert minutes and seconds into degrees then I am increasing the unit size to seconds Minutes brought minutes back to degrees I will do 15 point five, think it would be 60 minutes Is one by 60 degrees Unitary method yaar so 15 point 5 minutes how much is it 15.5 / 7 degrees

21:42 15.5° Write it down with a little love like this I can write 15 as 31/2 So this becomes 31 / 120, so basically 15 1/2 minutes means this much thing is 15 1/2 minutes How many degrees are made? 31 / 120 degrees are made. Son, this is 31/120 degrees right now So it was 45 degrees and then 31/120 degree and both of them got more Edward Take the LCM by 45 * 12 I hasten to hurry so that I will use the calculator to get the answer you don't have to do it brother

22:30 This is how it happened 1 second 54 45*12 A option has been created, okay, like this If you want to ask this question then please read this NCERT I am full of questions about the degree convert minutes into degrees There are three tax questions given, so I thought you can now There is no dearth of such options in this make it okay so this is an NCERT This is a level concept, let's move ahead Time conventions are increasing now see the most

23:17 This was the first thing that came to your mind as well hogi ki sir tenth and eleventh ka What is the difference in trigonometry? So I studied triangle in 10th as well so I am in 11th I am also studying in 10th and 11th What is the most major difference? So the most major difference is hey son what is the angle ok sir look at it brother till you were in 10th you used to sign tita a Perpendicular I had to study in triangle only They would go further by hypotenusing and always gives you a right angle If it was a triangle then it would always be a cute angle Was You have studied upto maximum 90 from zero to 90 till you took the tita also you took the tita Never taken it upside down straight out of the butt Now my son is the best in class 11th. It is important that trigonometry is

24:03 Children are angles no matter how old they are You will go from a cute angle through this right triangle Now we will take this angle out, We will still sign off at 120 degrees also sir what is this in this 120 in this no its taken out right its points If you think about the interview, Tita got confused Infact we will keep it negative also yes if you keep negative also then see it from everyone First, it is important to know the sign convention What is a negative angle? So what is negative and Positive angle depends only on this that if you have done the angle measurement then which direction is it ok It is possible that both of them are 30° but you can measure it like this If you are doing this then What kind of anticlockwise direction is this the direction is anticlockwise someone will come

24:49 I will do the same thing sir arra arra It is still important when you make the angle There was no importance of the ara, straight away The angle used to be 30 degrees but now I am hmm either it was made like this or like this he must have become major or else he must have done it like this this direction it Look anticlockwise, it is opposite to the clock This anticlockwise movement is like this If the clock is opposite to anticlockwise then this in the direction which is anti clockwise a blue What happens in that is what you call a positive angle So this will be plus 30 degrees okay but clockwise which is why clock The clock moves clockwise like this isn't it brother, time has passed like this, yes it has passed like this Sir we will call it clockwise, there are mines in it This too must have been 30 degrees but because

25:36 When it came clockwise it was called negative angle The difference between -30 and 30 becomes plus 30 I understood the difference by looking at the magnitude Obviously it's just a sign convention bro If I go anticlockwise then there will be plus angles If I go clockwise then the negative angle will be The sign convention is in anticlockwise direction In positive angle and clockwise major rotation There will be negative angles son Sir how do we know that it will come clockwise or Look at the negative brother, it's a simple thing for you either I will give you the erode direction or I will give you Aerodirection like here aerodirection is given what has happened here, what should I write on the initial side and write it on the terminal side Understand if you write initial and terminal

26:22 What is initial starting point what is terminal ending point Initial World means beginning terminal what does it mean and where to start from if If I write it here then it will start from here to measure and if I write the terminal there then If it stops there then it will automatically We have found our son, we have found him like this mother again this is 40 degrees suppose 40 so this It will become plus 40 because anticlockwise I can take whatever I want from 40 to 50 I am taking an example this will become plus 40 in anticlockwise now something Wise men come and say that Sir it's ok I had to do it from initial to terminal So I can do this too You said you had to go from initial to terminal This is the beginning, this is the end, so start here

27:08 and end it here done, if you do it this way then every This one is correct, the white one is also correct it's absolutely right it's absolutely right What will be its magnitude and what will be its angle It will be 40, if it completes 360 then it will be 320 but because it is clockwise Son, what do you say to this dog-320 degrees because the angle is measured in clockwise direction son is always taken as negative Remember, what is less sir, its positive Puri will look into the negative now Trigonometry is based on this even today For If you have any two lines then take a mother it's like this okay this angle is 90 so this It has become plus 90 and does anyone want to say anything or not? Brother this is I and this is T so tell me this one

27:53 so this one is you because it's clockwise and My magnitude is 270, it is 270 If it is there then it will be 270 mines, that's it Till now you were supposed to write 90 and 270, now write this 40 and I had to write 320 such things in the lower classes. what am I saying write it with pluses and minuses Right now one doubt that kids have is that Sir, what happened to these two? 360 is no longer an A If I do this minus 320 plus 40 then 360 is a It's not only 360 but also his magnitude What will come, son? These mines are just you don't have to take it with an angle I want to understand this, what is the sense of this You are mine because of clockwise sense just add the magnitude 320 and 40 then it will come 360 ​​370 90 add it 360 will come without If we add the sign it will come I hope

28:41 This much is clear mother, I will tell you I am giving you this angle, I am giving you this angle This angle will move you in anticlockwise direction direction or do it like this I gave you this angle of 50 degrees and I I am asking you to tell me this angle. Sign okay this is a simple question this is 50 plus 50 minus 50 I don't know I have given magnitude 50 to Erode There was no direction but it was with Ara If you ask, you have to tell me what this is It will happen brother, look, total two is 360, this is 50 If it happens then it will be 310, yes sir it will be 310 but it is clockwise yes clockwise so -310 Just apply it anticlockwise, it's in reverse direction, just cry If I had given it to you I would have said plus 310 and that's it It's a simple thing, son, it's anti-clockwise

29:28 Positive sign in clockwise negative in Just remember this sign, then your sign will be Convention became social and meant more than that If you go deep into this then there will be confusion Nothing will happen to you son, understand this much just need Come on let's see what's less is it ok to drive formulas negative angle formula quote of mines tita Now we define all these things which are of mine If you do then look I have tried to remember this I am telling you a very simple technique

30:15 of tightness and its reciprocal is SEC and SEC then mines disappears meaning kas of mines tita kas tita SEC θ will be in all the rest of the mines out will be a mines sign tita mines tan tita Mines Kot Teta mines cossack tita But why does this happen, see the logic behind this now I won't give you proof of the thing today. I will get it because for that again son these 12 13 15 hour lecturers will be made because after combining all the proofs, then What will be the benefit then, if you are in Arjun batch only Let's see, but we will clear the backlog I want to do that thing, I want to read less The one who has done the least in time then the proof

31:01 I will not tell the one who is not worth anything, okay It's no less than this, I just remember this The cost of keeping the mines disappears Mines in check disappears everything else If the mines are taken out then from now onwards no one I asked you brother sign of -30 degrees What is So what do you say dog ​​- Time Sun 30 Sun 30 If you have come to Sikar in 10th then mines are half it will go 930 half right like this what does this mean it doesn't mean anything in clockwise direction you will now see many This question must be coming to your mind, Sir sign tita negative how will it be 10th Till then it was time to get this thing out of here, friend Trigonometry power should not be negative because she was in a triangle sin30 There was a sign mine in the triangle 30 triangle I'm not there nine minus 13 maybe

31:46 Son, write anything like this 10 of -60° And mines come out in me too If -1060 and 1060 is √3 then -√3 is right click Off - If the mine is near 30 degrees it would disappear yes sir it will become 30 only i.e. this is √3 / 2 it will be tight - 37 tight 30 Right, this is called the negative angle formula. Now I will tell you some simple logic behind this I will give you the next topic if you understand then You should understand its simple reason You will wonder why mines disappear in the okay look i understand now So STC rule is a very important rule Basics of the ACPC Rule Tax Quadrants

32:34 This sign tells you all know it this is zero degrees well now you are a And many times you can understand a very sweet thing did you feel this way when you were a child I used to think that this is maths why does the first quadrant take it in that why don't you take this 1234 like this numbering honey chahiye one you three four like this should be or else 1 2 3 4 means in any situation we use it Why do you take the one on the right side and why do you take quadrants as soon as you You will understand son, what this is Positive X Axis Look it is moving in anti clockwise angle even 90 comes in anti clockwise direction you already do it major because anti How are the angles in a clock vice Son, I just told you that you are positive That is why you take it in the first quadrant

33:19 yes, such measurement is done because such If you do this then that negative angle will go to the right Do you start from zero or reach 90? We have to reach here by increasing from plus 90 Where do we reach 180 and beyond 180? Son comes up to 270 and from 270 Increasingly back to zero or 360 degrees one The matter is getting resolved, have you understood it by now You did not know that you were doing this if it's a line running like this So I will measure it like this only then the positive angle will be it will happen, only then you will give him first Such circular measurements of the quadrant mother you do it son Right First Quadrant Coordinator Even in geometry you have always seen this I agree that's why the logic was right, let's go now

34:06 In this we understand what is STC rule Basically we call it first Quadrants are fine, from zero to 90 Whatever angle I take it is spotless These are the angles of the second quadrant 90 to 180, take 100 degrees, then that second Quadrant becomes right third quadrant It is 180 to 270 and this is called Angles of the Fourth Quadrant 270 to 360 ok brother yes sir i understood ok look one And the funny thing is that I sign conventions I'm telling you right now I I told you that the angle can also be positive It is also negative, it is ok, even the angle is greater than 360 It is possible that someone has been having a mother like this Sir this is plus 40 let me make it here it is plus 40 so it is definitely a little right here

34:53 If you want to stop, turn around and go like this then this angle What will happen to the angle which is actually 360? It will be plus 40 meaning in any angle If I added 360 then it will rotate and become the same i.e. these two lines will give you 40 the degree was going, actually it was 400 degrees there is also ok brother i added 360 and once again 360 If you add it then it will be 760, it will be 760 degrees If someone says 40 degrees beyond the mean then I can add 3060 at any angle This is also a very important state angle in son 360 degree add or can be subtracted Let us come to the STC rule first Quadrants are the angles that have a

35:38 You will write S on this, you will write T in third You will write C in Fourth, you will write ASTC What is the rule on STC Rule A Stance Who what does this mean now Basically STC rule in first quadrant This tells you who is in which quadrant it will be positive, you listened carefully now I saw that brother negative values ​​also came and Mines 16 Who is in the negative first quadrant those who are positive in

36:25 In hotspots, anyone who is positive means trigonometry function take sine const tan Coat Sec CoSec One to 90 to 90 Degree And what is the range of spotrun from zero to 90 degrees are all positive in it If you say sign is 40 degrees then what will be the result Positive sign or tighten cost 80 degree I don't know the value but it will come positive don't know the value exact calculator I will need it but the temperature will be positive at 25 degrees Positive because in the first quadrant all are positive The sign is positive in the second quadrant this positive one is telling what is written The word 'no' is showing a positive sign Talking about the second quadrant, it will be positive I am late then someone can take me between you and 180

37:11 So if you take 100 degrees then from now on the Sun is 100° Now son, let us talk about an important matter till now What have you been studying Trigonometry since the 90s? Choti, now I am standing in front of the sign No matter how big the angle and degree I apply I will also define the sign of sine 100 degrees what will happen son because second quadrant is the angle of and s is written in seconds sign is positive 900 degrees will be positive what will be 100 degrees negative Because in the second quadrant the sign is It is positive, everything else is negative, good sign If it is positive then the cell will also be positive whatever is written here is from needles its reciprocal will be positive If it is written ten then the quote here is also positive If it is written then it is even positive So if I ask you

37:59 from that 110° now look at 110° again 90 and 180 In the middle of the story is the sign and COSEC Only people are positive, everyone else here is negative I have the right to ask the court 123 degrees 123 degrees also went in between then this will also be negative because the second Just remember this in the quadrant A Joe The one who is positive here is the sun positive here and COSEC is positive just 10 more quotes here Positive is between 180 to 270 and Quote is positive between 270 to 360 tech and its reciprocal cues are positive then Now if I ask you, let me see I am writing something you guys pause it

38:44 Thinking turn off 190 degrees positive or First look at the negative angle 190 The degree here is between 180 and 270 That means the son is positive in the third quadrant. In the third quadrant, it will be 10 It is positive that I have a degree from you Cost of 200 is in it again everything else is negative 250 degrees sign off 250 degrees 250 where is ₹250 between 180 and 270 in the third In the third, 10 Gods are positive and the rest are negative. take off 310 degrees are those 310 positive or negative 310 so sir

39:32 A score of 270 to 360 is given in the fourth quadrant In between and here the cash and stock market are positive Are All others are negative, this is the STC rule STC rule divides you into different quadrants Differentiate Trigonometry Functions It tells the sign for the angles ok sir Why is it like this? Why should I, my son, look at my life? I don't have time, I'll tell you in advance I am done, proof of anything is not important I will not tell you that, otherwise son this will happen There will be 20 hours of lecture remember this happens this happens In a way I got out of the right triangle Now we are putting any angle in front of it

40:18 Look, no matter how big the angle is, it's fine Now, I know some people might be thinking that sir mother please give me an angle bigger than 360 400 degree course of 400 degree asked I asked about 420 degrees sir, I remembered only 420 You have no one son, take out 420 degrees take me away what will happen then I will tell you right now I told you where it went in any angle remained I can add 360 degree angle to any It doesn't matter 40°, 400°, 760° If there is only one brother then in any angle if If you can add 360 then you can remove it as well You can also do 360 because the issue is the same, so 420 first minimize it to 360 eg two of this If it went 360 then it went back only 8 degrees brother

41:07 60 degrees is the angle of the first quadrant Actually it is 60, tell me it is half but In the first case, if it is positive then this I understood that it will become positive If he plays with you then you will make him small Make it friend, you can divide 360 ​​degrees out of it. You can tell by blowing it up, right? So it can be as much as one wants, any kind of random angle If I give it to you then you can tell me about it Mother take thousand degrees, someone says ₹10 degrees tell me brother is it positive or negative 300 years While flying I did a little 360 ​​turn bar 720 will fly what is thousand mines 720 it is 280

42:00 So this value of n thousand degrees is negative This is enough, give me one last example like this I give sine of sine of 2000 degrees but what happened keep doing this give 720 How much did you earn by doing bar mining 1440 Out of 2000 Can have as many as 14 mines

42:49 Now think how much is sine 200 degrees So sine 200 degrees is the same thing 200 so sir the angle of third quadrant is Ten coats positive in third Time will become negative, I hope now You have understood this, son, how can we Different angles in different quadrants Let's check the sign, it's telling me just that Don't think about it sir what will be the value sign 200 we don't know we don't know pass bus standard table same zero 45 30 45 90 60 is their value and so is everyone else's It is defined, we can tell positive and negative Calculator to give exact value I want it brother, I don't want it Can't tell the value right now

43:34 So now I hope this is clear now We are ready with this thing, second set off Formula set up first to read Negative angles right is the second set STC Everything on rule complete trigonometry 11th class is fine above Let's see now How to do it by STC rule Now we will read something about formulas People would not have even heard its name, Light what is angle sir there are formulas I don't know the name, look at the allied angle brother do you know the meaning of the word embraced allied I am your friend, you must have read it in history Allied forces sir yes very very allied angle then such angle is called allied Allied means friend what are those angles that There are friends whose sum or difference is less and

44:22 difference of two angles This 90 180 270 and 360 Angle yes you are a good friend like an example mother Take 30 degree and 150 degree what is happening with these two but their problem It is turning 180, there is a great difference

45:09 it could be 10 degrees or 10 degrees more 190 degrees, look what is the difference between them it is 10° 180 anything can happen Any of these four can be 1° and 89° This is also an alte angle because their sum It is going to be 90 right, take whatever you want take it friend 60 degrees and 300 degrees yes this too It is light because their sum is 360 take some such angles which are 25 45 degrees and 225 degrees or is it also old Sir because their difference what is happening the difference is 180

45:56 So basically common sense goes with Tita right brother the discussion is going on in degrees 90 because the sum of these two will be 90 or 90 plus tita right happened because 90 plus If the difference between Tita and Tita becomes 90 then I see this with these General Data Which ad angle will give 90 - θ - 180 ≥ + 180 270 - Tita 270 +θ 360 - Tita 360 + θ So this kind of thing which There are formulas, see, isn't it? Yes sir, now

46:42 I remembered this, see also in Physics - θ tight 180 + θ tan 180 2780 + θ such that Your formulas are called allied angles Formula understood it very quickly and very well I will tell you a summary of how allied angles come out because it is neither just In Maths but son, in Physics also very less Puri Maths 11th 12th is coming I will go into the angle formula later. I got upset, he is telling me a very nice trick So look now you must be thinking sir Just think how many will be made, sign it N Quote SEC COSEC All of this One year 90 - θ year 90 + θ all years 180 - θ all signs 1 2 3 4 5 6

47:28 7 8 1 went to the sign and formed an eight tightly formed eight We got 8 * 6 = 48 and 48 is what you got sir I told you chapter 50 is over, isn't it son? It is not 48, it is not counted in those 50 is in the allied angle of this one because You don't have to learn these 48 Formulas Did you understand how it became 48, look at the brothers Let my point go a little over the top, a little that remind me and listen to it because I The things I will teach you are a level plus I will teach you below your level, son. You don't need to go and raise your level This is what you have to get to the level of the level will not come down right that Let me tell you things if you want to understand the reminder from the cot Do it and listen to the benefit of recording again yes this is it so I was telling you that

48:13 Brother, each one has six formulas, right? This is the size of the sign and it is also 10 in it six in this six make it 48 8 seats now let's come There are 48 formulas, I will learn them no there is a very cute trick for that mother take any light angle formula Let there be a formula for any alid angle Write anything friend Write anything brother, I wrote it down wrote anything upside down left right I wrote any three taxes out of 48 and its a lot of love to drive it simple I am telling you a way If possible I will come, it is a very good thing

48:59 Hey, listen to Tita, what will you do first? Listen carefully while considering the cute angle I am not getting you to write it, you can write it down on your own. If you want to write from then it is not necessary for Tita cute angle considering tita cute angle Assuming this, find out its teta. has to be considered as a positive cute angle I am a mother to drive Formula There is no such requirement but to derive for this it is necessary to consider Tita as cute 10 If you get a degree then where did this 180+ come from 10 STC rule is less, brother let's make it Here Sir which quadrant did this go in is zero 90 or 180 or 270 then 180 + something so here something will go in third what is this Gaya takes out 360 from everyone in the third - Tita Ko It is best to take 10 degrees, yes 360

49:46 This is gonna come back If I mine this then I will be in fourth This is going to be fourth's 90 plus tight 90 just bigger than a second 270 Say Just If R goes right here then this also becomes A of third Understand the first step very easy Quadrant Take your attention to the second of these quadrants I heard from the quadrants that came in Sine STC Rule of Trigonometry Functions Time in the Third Quadrant according to What is sign A in the third quadrant In STC third, 10 are positive then the sign is negative or minus sign is stuck what is diya time son it is negative so here mines third quadrant

50:32 Sign Negative Cus in Fourth Quadrant Tight Fourth Quadrant gave but tight fourth is positive in the quadrant or put a plus Negative Cus Third in the 10 Second Quadrant I felt the sun when I was negative in the quadrant So the first step was to check the quadrant sa quadrant the second is sign check which There is a sign, it is placed in the quadrant Your last step is to stay on time Whether the function will remain or the function will change means this trigonometry ratio which is sine 360 is the difference between 180 and 360 You will go into logic sir, why is this so Why not like that brother even 15-20 hours are less Trigonometry is so big

51:19 I have no problem explaining the logic But for that you have to go to regular batch again You will have to look at the right So what will happen in this, this is also in physics By the way, you must have read the 180 and 360 ones which You can see it, keep the sign from it If you keep it then mines came here sun θ ho If the sign of the sign is tight in 360 then tightness and change to 90 and 270 How do these changes happen between 90 and 270 Son, such changes happen in both of them It is tightly packed in the sun with double side saw he gets into the court

52:05 In court changes happen in the sun in which sun then this formula If you understand how to derive, then you understand it If I go, I will do it quickly and write it down so that You screw him off son Let me write something else part of 270 - gives 182

52:53 Cossacks 270 + θ did you write anything friend that mother Write down the same charge again in three steps I will take the first step son Quadrant 270 - Tita Third 270 In Sign Negative

53:55 ok brother no great man is like this do that just open the bracket sir why didn't you do that to the year 90 + θ sir 90 bracket opened sir sign 90 plus sign Tita son, is this trigonometry a joke? the bracket is not opened Rocket does not open, any trigonometry sign nothing happens open the bracket of sun tita I have seen many children By mistake sir the sign of is A+B right? There is also a sign A plus then what happened sir sign Take in that which will become sign A plus sign B Son, my signature has no value to anyone You multiplied it like this then you are root why should I also do the root of a plus b Sir Root A+ which doesn't take root Even if you write the route, it doesn't work in it isn't it or does it not work in a + b² take the square inside because this is a function You don't normally tweet this function like this

54:42 can you do that you are applying loss of algebra Signs with plus minus multiply divide If it was bitter, take it inside, which is not for time can take it You have risen above all these things now. If you haven't woken up yet, get up now Come on if we understand the concept of light angle solve this quickly solve this quickly pause it's a very simple question yaar saree Find the value of right angle and make it sun 90 - θ sorry tan 90 - θ is first n 90 - θ First Quadrant 10 Change Tu Kot To Kot it will be bitter Second Quadrant Negative

55:28 Such sign of mines is tita Mines Mines are cut in multiples So this SEC θ * became Sun Tita numerator son became like this Right now a sum of 180 + θ in the denominator 180 + θ third quadrant nine third If there are mines in the quadrant then mines Sign Tita Brother it will go back to first place, something in 360 I added it, now people here call me Sir Tita why should there be a cut anything will happen yes but Cute mom's formula to derive It's enough for you, no matter what there will never be any problem, it will be ok don't you call this a first quadrant mother's Just drive, it will always be right

56:14 Hot 360 Plus will remain strong mine came just once basically look at this Mines did not come in it Mines did come in it In this both of them had a mine cut There is a plus in this, there is only one plus in this mines went out answer is done mines one c Option C is the answer son Right Like This So now this is our table for this old angle

57:01 Based on the above you can calculate the value of all these very easily. We can write the time constant in 120 Now in 135, you have to go upto 90 and then upto 10. We are extending this first 180 till now you are doing right So first I will tell you the method, then You also like its trick method which is very good I will do it and tell you right like mother take 120 We have to find the allied angle of 120 x 120 What can you write in terms sir 90 plus I can write 30 Ok Positive in the second quadrant

57:50 Take out whatever you want now, something great The person says that sir we why should we write it like this even if it is 18-60 Brother, you can also write 120 as 180 minus eight you can write it there is nothing wrong it is absolutely correct Is Write it like this bro so what will happen the sign will not change with the sign 60 will go fast its 60 sun 60 again is √3 / 2 ok yes so here it is √3 / 2 sin120 came, you can take it out as you wish brother what is the story of this lok of d story Write the light in the up as you wish

58:35 It doesn't matter 90 + θ 180 - gives Write your final answer as you wish it will always come from ok yes sir i understood 135 150 in which Write down your wish, okay let's sign 150 or let's go I will show you how to do 150 I want to make you happy but I will give you a hand I am showing you the rest you can do yourself at home. What will you write for 150 in NCERT? 180 -30 - If yes then mine will go to route 3/2A -√3 buy you the value of 150 Correct

59:23 why are you doing such a long method son because we have to show up at school too right but now i will tell you the trick method I will give you the medium through which you can write everything There is no need for you to move this table from the cot People will file it just like that, sir yes just leave 180 and keep the rest as is Sir please tell me how to file it, sir I will tell you right now yes my friend look here Brother first thing is to try this folk method Forget the 90s, I swear I will make you an ally If I make it then it will not be with 180 or 360 So I will not make it, I will leave the question sir I would not have done it otherwise I would not have made the mistake of doing 180 I will join you in this particular quadrant So it is definitely 180 but not 360 There isn't that big an angle yet I will reach further in the next 330 till here

1:00:08 When I reach there, we will talk about 360 as well but for now i am going to stick to 360 and 180 only I will do the 90s, I will not lock him Methods with I have done it correctly in objective method listen very carefully to what i am saying hey love method 120 First sign with STC rule then you will know It is 120, see, time will come positive Time will be positive or negative 10 will be negative 120 because seconds The angle of the quadrant is STC rule sedge and sign positive cost and 10 negative and now 120 So see who Allied is with doing 180 whose friend is this sir 120 is a friend of 60 because with 60 Allied is 60 and 120 sum to 180

1:00:55 And he was also with 30, he is with 90, 90 why shouldn't he do that which one should he do is 180 degree turn and its light angle is If it is 60 then paste the value of 60 But that is the method, that is the method So that's it, we're just doing it orally now what do we do we are watching let's hear it again like 150 for 150, with whom do we do it first? Look Sign Sign Positive Second Quadrant I have this negative and 150 with whom is the light 30 with 30 degrees so 30 degrees Paste the value of , here is 30 degrees The value of 1/2 √3 / 2 1 / √3 is 150 + 1/2 is 150 mines route 3/2 tan 150 - 1 / √3 do it in 135 also

1:01:42 this logic will not apply in 180 this logic will not apply in 180 we will see separately what will happen and in the butt rest Extend it as much as you want, look everywhere these ones told I have told you these three for 180, I will tell you for 210 Let's apply the same logic to 210 Are I will write 180 + 30 This is from the third quadrant, see, there are 210 of them The story of the third quadrant will be in the middle The angle is sun negative cuz negative ten positive

1:02:29 So what did I apply Mines Mines Plus Just paste the value of 30 degrees and you can see the root 3/2 so half here here root of 3/2 mines with and here plus one by root of 3 so 10 210 will be plus one by root 3s I am saying this Orally we take out Rs 240 from this also Let's go out You can file it using this method which comes out to be Rs. 240 I will take the remaining children for you I am getting one or two out to understand Who has the right for 240? don't do it 270 do it 180 or 360 In this I will write 180 + 60 in the third i.e. 60 with A light and 240 in third Mines Mines Plus N is positive in the third quadrant

1:03:15 Text value from STC rule I'll do one more He has to do 180 or 360 using this folk method If you want to do it like this son, someone please do it Obviously this thing is valid for this separately

1:04:03 will have to do this because boundary point is gone We will have to look at 180 and 270 separately because what are these other points 360 There is no difference between 360 and zero If it is with degrees then it is the table of zero will stick here 010 0 degree right butt in 180 and 270 Now let's see what we will do Brother, we will do the same, the basic method is egg This is it, let me take out 180 and show you Do you want to tell me the cost, how to take out 180 I'll get one made, see which one is fine Rest of you just keep going on 180 He will be some great commissioner sir i am 180 - 0 I will write ok someone will be there sir I I will write 180 + 0 or else it will be 90 + 90

1:04:51 It will remain 270 - 90, write it as you like I am telling you that the answer will come from The only difference is if you do 180 - θ is written like 180 - 0 look 180 me I know nobody has it on rent Brother since when did 180 start being in the quadrant 180 so here is the second and third exactly between But if you have written 180 - 0 then this take second consider second quadrant This But what is this about applying formula here? For this we will consider only seconds 180 - Tita second I consider myself a son And in which second it becomes negative sir yes there are mines what should I do now how will the mines become sharp

1:05:38 That means mines zero will become zero zero one If it happens then that means -1A will go -1A will go to what 180 Now I know you're thinking Sir 180 It won't make any difference if you write + 0 brother If you are writing 180 + 0 then its third Taking the quadrant mother because 180 + θ I also consider right 180 + 0 as third Will you accept the third? Is there any negative in the third also? Is The answer will come from here only, brother. The answer will come from here only. Mines One will come down in the ditch cost of 180 mines one happens okay so I am filing this table now. You have to take it out at home and verify it I have to do a 180 sign, vanity will come to zero this mines one this zero mines one in 270

1:06:25 Zero and Note Define Fix it like this in 270 as well If you want to take out sign 270 then you Write down 180 + 90 and 180 + θ Sticking to the Formula Considering Third Quadrant If you get the answer then I will tell you I am saying the formula is always valid no matter what be anything but always all the stars are valid Ok

1:07:25 okay brother if a plus b has a degree relation And the sine will be equal to 17 degrees like this why to do it fast in objective Because what is the sum of these two? 180 If the sum of the two angles is 180° then It remains to be seen that their signs will be equal yes, I will prove it right now, sign of 25 degrees and sign off 165 degrees sorry 150° will be from Because it is related again brother Sign of one degree Sun is equal to 179 degrees because their vanity is fine Why is it like this? It is very obvious friend.

1:08:10 see from here a + b180 - b Sign A Sign 18 Will be done right can I do this sign p by 7 And the sun will be equal to 6π/7 sir what happened how to do it in radium with p / 7 7 by 7 then it is pe pi meaning It is 180, which means this is also absolutely correct.

1:08:59 Did you understand son, then I will say Sun π/14 and Sign 13 π/14 is this it yes definitely friend Equal There is a lovely property in Pause too what is the sign of a if a + b is 180 So they are equal but what is A times what is B Will be done I understood why you understood my friend, not me sir I did not understand, I will tell you now brother because when I take the cost on both sides 180 mines b has mines b What would be negative in the second quadrant?

1:09:45 There is just this much funda, then in all this if If I wrote this down, a mine would pop out should I give him 10° what can I say to him dog Mines X 170° If you say 180° then the cost was 30 degrees The sum of two angles will be equal to if 180 yes times are equal in which case mines are outside It comes very rarely, this right will come like this and You understand what will happen friend, body 180 - θ also - the body becomes bitter inside the body also - outside will go right yes now exactly the thing you You can extend it to 360 also if a plus b is 360 so guess what can I say to you and which will also be equal

1:10:31 Because you understood friend 360 - Tita Kas bitterness is the right example Think 27π/14 by 14 and 27 times π/14 cut how much is a So it is 60 because it is 5180

1:11:17 It is 360 i.e. you get the sum of two angles if it is then it is tight and equal, simple like It's simple friend, it is a combination of two angles The sines of two angles are equal to one and the sum is if it is 360 then what are they equal to, okay I will change it to degree if 510 degrees is equal to what? 350 I want to say that it will be equal to a degree I This much is clear now look at this small thing It is a big thing when it comes into question It hurts so much that I don't understand what was happening let's put it into question Let's find out the values ​​once first To simplify, we have to write sine 11 π/17 on this What is dangerous, you should not do this Look, this is 11π/17 and its brother is below

1:12:02 look here it is because from 17 17 down in this what is going on between these two see 11 to brother 17 + 6 π/17 17 so LCM is orly 11 plus 6 17 Their sum is 17π/17 That is, it is happening on otherwise it is from sun tita sun e = all it means these two signs this brother of it It will be cut with this, this is how to do it orally Understand - If it comes out then they will bite butt Vidm-1 because 10 p mines tita mines ton tita

1:12:49 It happens son and 11 3 14 14 brother 14 then who will be in it If mines come out even in the case then this Both will be cut but one mine of this too mine one will come in mine one will become one Understand the matter from someone else next time you will be very clear will then remind yourself to do it first and then from here also we see this is his brother this what is the sum of both Sir, both angles are settled in 2023 What is it? I just told you, if it is on A + B a+b180

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