Trigonometry L-4 | Double Angle Formulas | Class 11 Maths Chapter 3 | JEE Maths | JEE 2021 | Vedantu

Tell me once aga Can you hear me and see me Type yes in the chat box this time So that we start with one of the very important sets of formulas Yes double and triple angle formulas To 11 it's time for your daily dose for class 11 Yes we are on part number 4 matlak ki if you go down in the description box of this video To pehle ke 3 parts aap dekh sakte ho And I would personally recommend that if you didn't watch it make sure you're watching it after this video We will start with double and triple angle formulas today So as promised formulas and questions are now more frequent in the new format we are following This is the Vedantu Math Telegram group You will also receive the link to the group in the description box of the video It will look like a name appearing by joining the chat Everyone you can click on that and join the Vedantu Math Telegram group Here you can also find all my free PDFs from the session Secondly you will be notified each time I am online I just want to connect with you about anything anything at all This is one medium where I keep doing it Alright make sure you're part of the Vedantu Math Telegram group as well If you're targeting JEE 2022 kids Then this is the link YTJEE22 The link is also in the description box You can click on this and enroll absolutely for free Okay so let's start guys Everybody how is the josh here in the chat box Yes tell us quickly is the josh high in the chat box So that we can absolutely start the session and tell everyone boss that the class has already started come on in Whether you are preparing for JEE for any year 20 21 22 You want to take your CBSE ISE exam Or are you preparing for NDA This class is very useful for everyone Kyuki in class I'll be teaching you formulas along with tricks to learn them let's move forward So this is the first set of formulas Here you are talking about double angle formulas So let me just take you a little back So double angle formulas we are going to look for the formulas for sin 2 theta cos 2 theta and tan 2 theta We solved three formulas yesterday Okay we solved three formulas yesterday Which are your compound angle formulas Matlab sin a plus b cos a plus b sin a minus b cos a minus b And in the same way with tan I said that you just need to remember one formula the rest are all derived from it and I was absolutely right about the children Because here sin 2 theta if it exists can be written as sin of theta plus theta I can write it as sin of theta plus theta And here we can now apply the formula We know This is sin a cos b plus cos a sin b Main taught you tricks to remember all these formulas Make sure you are watching lesson number 3 if you have missed it So that's what it's become As I always say don't just look at the formula and wonder what it is just understand what the formula is trying to tell you So feel the formula is the new thing So always feel the formula what it is trying to say That means it is trying to tell us that sine of 2 theta If you have a double angle then if you have any angle that you want to halve Listen carefully again any angle you want to take you can use this formula it jumps out twice Come on everyone jump with me Just write jump in the chat box Because if you want to halve any sin's formula Tell him to jump out he'll fall And sine theta cosine theta it will split Yes everyone understands this Amazing let's go ahead This is the formula we need to remember Now I should apply Hey we shouldn 't become a poor beggar We don't have to be kids we just have toe the line Ki bhaiya theta hoga tabhi hum formula ko samjhenge I would like to ask you kids If you see sin 10x how will you split it Type a little in the chat box If 10x is divided how will you split it Let's see how many are left Give me the exact answer for this If you are given sin 10x Going by the same logic I need a breakup in half Half a breakup is needed Watch now as I explain The children wrote the answer completely wrong How many of you wrote this 10 sin x cos x Tell the truth now Because students mostly write this way 10 sin x cos x When they are learning something new they write this down Listen I said something Listen carefully to this Your 2 will jump out I didn't do this If the number is out it will jump out No no 2 will jump out That means you can write 10x as Twice of 5x You understand Twice of 5x And you will jump again 2 Got it kids That means The correct answer will be 2 sin 5x cos 5x Hurt yourself Monday to Friday All the topics that are in your tricks I will take the test on Saturday Make sure all the children come For the test on Saturday morning Okay Understood Logic understood This is your double angle formula So take it like this and send the number outside Only 2 more jumps in the spring One more question I have for you Let's check one more child And let me see how many of you Give me the correct answer Okay Okay so I have 2 sin heart cos heart Tell me the answer Let 's see how many of you Give me the correct answer for this In the chat box Yes in the chat box Everyone Right Because it 's necessary to understand What' s going on The kids have said Ma'am see So you should know the formula To and fro That's fine So If you want to take it back You want to collect it back So this 2 will go inside And shut it down Your heart will be broken Friend this was just an excuse To take your heart away Everyone So you know This love is here You can hit the like button To show the same love That you are giving here Okay Now someone is asking me The question Miss How would you split sin 7x Quickly send the split Everybody sin of 7x Let me see Yes Let me see How do the children split up Remember That' s the one that comes out It's only two sirf Nothing else comes out Only 2 comes out Ok So here You How can you write You will take this 2 out To divide 2 sin 7x by 2 Cos 7x by 2 So nothing will happen to you You should know How to actually do this Kai bachon ne Sin 3 5x Cos 3 5x Lika Absolutely fine Yes Absolutelyfine Yes Biswa This is very Important concept O Everyone understands this thing Amazing That's the story We did it in cos 2 theta Cos 2 theta guys If I apply the same formula Because of theta plus theta Yes I can apply the same formula Because of theta plus theta What will happen in this How do you write in this Cos a Cos b By plus hai na So this minus rebel Sin a Sin b That is this becomes Cos square theta Minus sin square theta Everywhere bachon Everywhere Whatever your hape is Angle is it becomes half Understand this concept Very very well Cheeke Ok Some questionsremain Why minus beta You need to watch the previous lesson 3 We discussed all of this in it Right Same way guys Same way Now look here If I don't want it I need the answer Completely in cos squared x Toh isko main 1 minus cos squared theta Likh sakti hu That means The answer ca Converge to 2 cos squared theta minus 1 If you remember a formula you can do the rest It's only the modifications Same way If I want sin then this 1 minus sine squared theta That is 1 minus twice Of sine squared theta Everybody Do we understand Yes ChildrenEveryone understands this We've got it Yes or no In the chat box Okay You're on it Take an example If so As in An example I can see Tell me again Angle half It happens Someone is asking me Ma'am Because 5x What will happen I would like to ask you Look Whatever you wa You have to make a formula You can make it It's your choice Depends on Sometimes what happens The question is asked Whether Prove that this And a poor answer It is done in Sin ki terms Then you know You have applied this formula Otherwise We normally stick to The first one only Okay Tell me what 5x is What happens to 5x Going by the first one What will happen It's going to be Right away Cos squared I will halve it 5x over 2 Minus sin squared That's it The question is done It's clear to everyone Everyone should It's important to you Both formulas Reversing and applying should be done It's supremely important Yes Yes guys Chale aage Chalo Tan 2 theta ki Baat karte hai Again Yehi wala formula Aap laga hoge Tan of theta plus theta Hain na The tangent of theta plus theta We'll put The tangent of A plus B What are we going to write So tan theta plus tan theta is 2 tan theta upon 1 minus A into B This is Amara's lovely formula which we' ll remember Yes Everybody Again look at Tan 2 theta I split it as Theta plus theta And that whic Tan A plus B is the formula this is it Everybody Yes Here comes everyone'sanswer That is why Kids I keep saying again and again Watch every session to make sure you don't miss any concept as every concept is built upon the previous two concepts Yes guys everybody We follow this Let' s That is what have we learned so far We have understood This formula Sine of double angle What was simple The simplest to Sine theta Cos theta = Ok = Cos 2 theta = You can have 3 formulas = But = I am writing only one = Because the others are just adaptations = And finally = Tan 2 theta Okay are we following all this Yes everyone understands This is making sense Let' s go Great Amazing These three have become formulas Now let's go ahead and check what else you want to do here let's see you Small proofs also exist I can discuss everything with you but what is my goal all proofs are there Books also give me something you know That should be understood here Okay Now let's understand That I mean this Even 2 theta I have taken it Let's understand This is also These are 2 examples That Now look Understand And I will also explain the method of remembering it later Sikhaungi Sin 2 theta yaar We just did this formula 2 sin theta Cos theta But this can also Have a formula In terms of tan Derive it How to do it Let's understand that Okay And here Cos 2 theta Was my Cos squared theta Minus sin squared theta Also In tan How to derive it And yeah Main I already know it' s already in the tan Okay It' s already In tan So Very Important again Dhyan se samjho Mujhe isko Pura tan mein Change karna hai What can I do Yes Can I write this As upon 1 2 sine theta Cosine theta Upon 1 Bache kahne Divide by cosine theta Beta that won't help Hai na We need to completely change the tone And this forest this forest is I K Ray's amazing wave writing for childre One minute sin squared theta plus cos squared theta can be done What else can we do the children are getting bored Turn off the lights in the Mama Cos Square theater and tell me Let's leave it I'm not saying anything right now you tell me I want the answer to this how to get it Tell me how should I get the answer to this Yes let's see 1 plus tangent squared theta yes How will I get this answer How are we going to do this No Hitesh we are starting with your questions on the set This formula after this Yes divide by cosine squared theta What happens after dividing by cosine squared theta This will become tan theta this will remain cos theta Tell me think about it for a minute think about all the children how would you convert them here Yes kids let me see how many of you can think about this how you would convert it Yes write one as sine squared theta plus cosine squared theta Of course that's exactly what I was telling you from the beginning You can call it sine squared theta plus cosine squared theta over one Correct now divide by cosine squared theta Now just divide up and down by cosine squared theta what will this become 2 tan theta over 1 plus tan squared theta the question is done Tika the question is done And I should also remember this formula I will teach you the technique to remember it now Everybody yes we have done this great Come on kids let's go to cos 2 theta Cos squared theta minus sin squared theta I will also divide it by the same thing What will come up in my case if I take the tangent squared theta plus one and then divide by the cosine squared theta 1 minus tangent squared theta over 1 plus tangent squared theta that's exactly what the answer is And we have already derived it in tan yes or no Yes or no in the chat box kids yes everyone we understand this Now just understand all these proofs will be given to you how to remember them in terms of tan x Ma'am this is a big confusion how do we remember all three formulas in tan Now I am going to tell you a technique listen to this from Dihan you will remember it You will only remember one formula children just one formula the sine formula Sin 2x is 2 tan x divided by 1 plus tan squared x that's the only formula you are going to remember No source language words "Derive" is okay as it's a standard English word Proper nouns None here Punctuation: The original has a period so in English it should be a period The is a fixed marker so leave it as is And kids what happens in tan You have to write it as is in tan just write it as is in tan as well But tan is the composition of sin x over cos x some negativity will come into tan That's it that's it guys tan 2x has already been derived 2 tan x over 1 minus tan squared x and the question is solved Yes the question is absolutely dead you can remember it like this and you don't need to remember it for cos 2x We know that tan theta is sin theta divided by cos theta right That is what will my cos theta be sin theta divided by tan theta right Sin theta divided by tan theta what is sin this is what I have to do first divided by second In the cosmos first comes negativity it's a very rebellious function this will be the answer All you have to do is remember just one thing the rest are just modifications that's it yes That's it kids all we have to do is just one thing as I've explained before Everybody everybody yes Are we clear Are we excited for the questions Are we excited for the questions now Okay But before the question some children were writing the half-angle formula now understand this it comes from here there is nothing new in it What is the half-angle formula If it is sine A then it will be twice it will become A over 2 cosine A over 2 I've already discussed this with you guys children Same way if cos A is there then it will become cos squared A over 2 minus sine squared A over 2 And you'll think oh my god I don't know what formula this is right It's the same thing there's nothing new here understand There's nothing new here okay So the same thing here is just what you wrote and it's called the half angle formula What I first discussed with you anyway right Let's start killing the questions is my army ready to kill the questions now So 3 2 1 let's go come on How are we going to prove this How are we going to prove this kids Sudhanshu stay tuned kid you'll get the answer to your question right away okay Let's start with secant 8a minus 1 over secant 4a minus 1 you have to prove it is tangent 8a over tangent 2a how can we start Many children said "Ma'am at the beginning you can change secant 8a to 1 over cos 8a " and same way 1 over cosine 4a okay Now if I take the LCM this is 1 - cos 8a 1 - cos 4a cos 4a goes up and cos 8a comes down right guys Everyone right Now I'm going to do the thing with you basically we are going to apply one such thing kids In which you will use it in limits derivatives integration basically the entire calculus This thing is used repeatedly even when we do inverse trigonometry Listen to this carefully how do I change 1-cos 8a Tell me how do you halve the angle of cos 8a Write in the chat box how do I find the half angle for cos 8a The formula for cos 8a the way we have been discussing the formulas Let me see how many of you can tell me yes Then the children started writing ma'am cos squared 4a minus sin squared 4a okay yes I can also write it this way yes basically what I'm doing is using it this way I can even write it as 2 cos squared 4a minus 1 I can even write it as 1 minus 2 sin squared 4a understood yes kids we got it Now which formula do I need we have to think about this Which formula do I need kids I need to think about this one Now watch carefully I need 1 minus cos8a and I know there is a tan here So that means I need sin in my life cos it's already there I need some sin Look at sin what can I write from here if I choose this formula this one Look carefully what does 2 sin squared 4a become 1 minus cos 8a Yes or no in the chat box 2 sin squared 4a can be written as 1 minus cos 8a and this is very useful So basically these two formulas are very useful because they help me in converting Sorry this one and this one that is this helps me in converting Correct you understand 1 minus cos8a I can write as 2 sin squared 4a this will be cos4a Now if you've understood this concept tell me what will happen Tell me in the chat box I mentioned this 1 - cos8a what will this 1 - cos4a become Come on guys tell me in the chat section let me see Let me see how many children do you tell me about Yes how many of you can yes Ritika is the first one followed by Tauseef Anish Sure sure Vamsi absolutely man it was 8 here so it became 4 Here there is 4 so it becomes 2 we are actually taking the half I see yes everyone has understood all these things Bit You need a lot of practice in Trigo so we are going slowly So look just cancel this what's the result will I get my answer from this Will I get my answer children look here what I need to prove So let me sort out my RHS a little Yes my RHS is guys what is this this is basically sin 8a over cos 8a and this is sin 2a over cos 2a what have I already received Look here I already have cos I have found cos 8a here I got sin 2a equals 1 which is a big problem because it's cos 4a And this is sin 2a 4a still what can I do kids what can we do with this Now look carefully I have already received one thing I am sin 4a if I write sin 4a like this Okay I'm splitting this sin 4a sin 4a and this is cos 4a upon what is this mine let's go to 2 let 2 be as it is 2 is not cut and here is 2 sin 2a x cos 8a now look carefully at what we are doing Can I take this please pay attention 2 sin 4a cos 4a If I take 2 sin 4a cos 4a can I get sin 8a has this become clear to me Yes or no absolutely sin 8a will become and sin 4a as it is and what is coming down to me this thing as it is Okay one more thing to check you don't have sin 4a anywhere Sin 4a is nowhere this thing is not happening Then I will also split it into 2 sin 2a cos 2a If we also split sin 4a into 2 sin 2a cos 2a Now what have I got children I have sin 8a I have got cos 2a I have got cos 8a okay One sin 2a will cancel out here two is cut that's it I have my answer Yes 2 sin 2a is cut off above and below and the rest I have my answer Yes or no yes or no okay understand again Yes listen carefully again and understand what we have done Very very quickly children and then we'll go ahead okay understand this once secant 8a you wrote this down 1 minus cosine 8a and upon cosine 8a this will come here 1 minus cosine 4a over cosine 4a okay this is your left-hand side what we have is the left-hand side is this What's your RHS keep it open too sin 8a over cos 8a okay and this is sin 2a over cos 2a right keeping the target of what I need Okay so cos 8a is already in my notes 1 minus cos 8a can be written as 2 sin squared 4a This becomes cos 4a as it is and this is becoming 2 sin squared 2a okay Now you have to split one by one learn how to split carefully Mix it with 2sin 4a okay let it play one of them Okay that's it don't do anything to it leave it as it is This is all done for you sin 8a that is I have both sin 8a and cos 8a Okay sin 4a is not needed so I can further split this as 2 sin 2a cos 2a okay 2sin 2a cos 2a now 2 cut sin 2a whatever is left is the answer That's it the one that remained is the answer so all these things take a little time to understand You have to memorize the question someone wrote ma'am you have to memorize the question you don't have to memorize the question You need to memorize the formula okay everyone this is the next question kids You have to prove that this side is equal to this let's check this let's check it guys How to do it LCM absolutely right the kids are saying ma'am ake LCM take LCM for the left hand side so what am I going to get cos A plus sin A squared (cos A - sin A) squared divided by cos squared A what would that be minus sine squared A simple I am just taking the LCM kids what will I get what will I get here Yes what is coming into my LHS cos squared A plus sin squared A is 1 I will get 1 plus 2 sin A cos A and here guys cos squared A plus sin squared A which is 1 minus 2 cos A sin A how are we going to eliminate this further 1 cancels out with 1 what am I left with yes someone told me something really interesting cos squared A minus sin squared A what is this does anyone remember the formula Absolutely right guys this is your cos 2A yes this becomes cos 2A and what is happening here above guys 2 sin A cos A is sin 2A which is also your sin 2A so what are we left with 2 sin 2A over cos 2A That means we have reached the answer directly and the question is done okay Then every question takes time someone gets it very quickly It takes a little time but you have to understand so keep revising Because Saturday is coming with your very special mood okay Okay this is the next question kids on your screens now take a look how can we solve this one Yes let's check this one how are you going to do it yes how are we going to do this square both sides No you have to prove this it's not already given Now look this is a very popular question When exams are held at your school it also occurs in JEE Even in the NDA you will always start with the innermost The one that is the innermost square root you start with that and now understand what happens Now the same formula which was taught a little while ago Is cos2θ expressed in terms of cos because my answer is in terms of cos If it is 2cos2θ-1 then kids tell me one thing cos8 which means that from here 2cos2θ is 1 plus cos2θ everyone understood this How did the conversion go yes this is easy now how do I children look at this If I have cos1+ which is given as 1 plus cos8θ what would happen if there is 1 plus cos8θ Let me know in the chat box if 1 plus cos 2θ becomes 2 cos 2θ Basically two jumps make the weight come 1 plus cos 8θ will become what yes Prajval Mridul absolutely Half hour stay the angle is becoming half that's it 2cos2 4θ absolutely right what did this become at means kids this will become yours 4cos2 4θ That is 2cos4θ everyone understood this has only just been solved inside I need to go out again just one more time They will go no issues now we are considering the second bracket but at least we understood what needed to be done here so if I consider the second bracket now 2 plus this has been solved as 2cos4θ ow the same thing yes the same thing we are repeating children I can take 2 common 1 plus cos4θ okay that means what will happen now I want to know what this will become can someone tell me what will this become 1 plus cos4θ this Vamsi absolutely Alekya A lot of you are telling me ma'am 2 cos 2θ got it at means it becomes when it comes out of the root 2cos2θ each time you can see 8θ 4θ 2θ So you know with the next one we'll reach our target theta right So one more time Now the last one 2 plus 2 cos 2θ go with the same logic kids s is going to be 2 cos 2θ which means 2 cos θ and the question is done everyone yes or no in the chat box Look all these men are being done just for you You have to keep clicking the like button if you are enjoying the video Let's evaluate tan 22.5 degrees how will we do this Let me see how many of you can get a tan at 22.5 degrees Yes kids are we ready to kill this tan 22.5 degrees how will I find this 22.5 means the children have identified it this is the tangent of 45 degrees divided by 2 correct tangent of 45 degrees so let's do this Look can I write this as tan 45 degrees over 2 Yes or no in the chat box can I write it as sin 45 degrees and cos 45 degrees Yes or no in the chat box yes absolutely sin divided by cos we can write ow the same formula that was just mentioned cos 2 theta is 2 cos squared theta minus 1 that is 1 plus cos 2 theta is 2 cos squared theta Again and again I am repeating the same formulas children understand same way I can write this as 1 minus 2 sin squared theta That is 1 minus cos 2 theta equals 2 sin squared theta yes or no in the chat box yes here it is How do we solve this let's see Everybody watch this very carefully what's happening here That is if I have sin squared theta if I have sin squared theta I can write it as 1 minus cos 2 theta over 2 is equal to sin theta will be square root square root of this plus or minus what should I take Because I did not square Whether it's plus or minus I can handle both Tell me kids can I take plus or minus both or only one of them let me know in the chat box let me know plus many children wrote plus why why only plus why not minus Yes a lot of you are writing both as well why is plus the correct answer because this angle is in the first quadrant Okay we don't have to forget our basics it is in the first quadrant so it can only take positive values Yes no negativity here that's why only plus okay only plus same way kids ere cos theta what will I get same logic Only plus correct only one formula left people and we are only using that again and again so here see sine 45 by 2 I can write as 1 minus cosine 2 theta over 2 that is 1 minus cosine 2 theta that is 1 minus cosine 45 degrees This one will be 1 plus cosine 45 degrees and of course 2 and 2 will cancel out We understood this much yes or no did we understand this much kids yes or no Yes I understand the same thing now cos 45 and cos 45 can I put the value Can I put the value for cos 45 yes I know the value of cos 45 1 over root 2 Yes 1 over root 2 You solve it what will I get root 2 minus 1 over root 2 plus 1 if I rationalize I will only be left with root 2 minus 1 which is the answer yes if I rationalize It's not clear Yes or no yes I understand this am I using a lot of new formulas no I am using the same thing again and again children same cos 2 theta formula again and again okay You must definitely practice this let's move to the next question guys s is another method if you use time but then this is certainly very long but if you want to this is an alternate solution sine 7.5 degrees It will now seem easy come on sine 7.5 degrees Let me see how many children tell me this sine 7.5 degrees What will happen that means this is the sine of 15 degrees divided by 2 alf angle can I find sine 15 first how do I find sine 15 degrees It was just taught yesterday Tell me in the chat box how would I start with sine 15 degrees Well done Come on kids yes sine 45 minus 30 exactly right can I calculate it we can calculate it what will happen sine A cosine B minus cosine A sine B Okay that's what I get which is 1 minus root 3 over 2 root 2 sine 15 degrees is this much yes sine 15 degrees is this muc ow to calculate sine 15 by 2 the same formula this is 1 minus cosine 2 theta s equal to 2 sine squared theta The formula we have been using for so long yes we are only using one formula some children I think you are rationalizing that 's okay that's your choice yes that's your choice here it comes buddy meaning my sine theta again 15 by 2 is first quadrant sine theta will be root of positive root of cos 2 theta by 2 Okay so my sine 15 by 2 s 1 minus cosine of 15 degrees over 2 instead of sine If I had taken the cosine my answer would have been easier Yes because I am looking for cos here Then there's no problem buddy because it's going to be much easier because 15 degrees same story cos 15 degrees same story cos A cos B plus sine A sine B Okay so root 3 plus 1 that is instead of cos 15 I can write root 3 plus 1 over 2 root 2 the whole thing divided by 2 just simplify this and that's your answer yes we just need to simplify this and that will give us answer Wait son don't grow up yet They asked me a question actually it creates a lot of confusion In children's minds so if I want cos like the previous question was 22 and a half degrees isn't it said the child ma 'am cos 45 degrees 1 by root 2 is cos 22 and a half degrees should be half of this this is true or false Tell me if I can do this job True or false in the chat box Because many children tell me They will laugh now they will write false things But this is a problem for many children What's the difference I've halved the angle here I just halved the angle You've just halved its entire value This means that if sine 90 degrees is 1 So sine 45 degrees should be 1 by 2 yes or no Sine 45 degrees should be 1 by 2 We don't even need all these formulas Yes don't do that this is not true but this is a mistake Children I have taught throughout my teaching career I have seen it many times many children do this okay let's move forward So that's what we had done I am sure So trying to calculate sine here didn't help The benefit was worth it the cost was worth it okay let's go Before I go ahead kids Here are the features very amazing right for example look here The teaching that is happening the life teacher who is teaching with him You can obviously ask them questions there is also a parallel teacher Those with whom you can ask questions together Those that do not appear on the screen but you can type and keep answering in the class I mean life quizzes and all this is a part these quizzes leaderboards that you see This is just a part of our regular classes right and here you get a very amazing feature okay which I call my calendar So do you all also read like this calendar For your JEE 2020 it means week-wise here Everything has been read what to read in physics What to study in chemistry What to study in math Yes So it is super duper important kids that you are read to every day That you are going to read we put you in that regularity this is the USP of the course and secondly children which is a very amazing thing What you see here is just the beginning You get access to your content library right Then your crash course will be activated For example go to math though this is true for physics chemistry math along with all of them If you go to math here let's say you have an assignment on sequences and series You are taking a test it is a test in the style of JEE JEE style means you get a question Along with the digital OMR sheet how you can apply okay So someone marked the answer wrong How to change it It's just like your real JEE paper so a lot of real feel we are trying to give you over here f you are interested and I always say the same thing as a family Okay as a family member if you're interested If you haven't joined the momentum yet then This link will be found in the chat box vdnt in/jee-cce You can apply code to this my NAGCC That's Neha Garg's crash course and you can get physics chemistry math all three of them at this price Okay so just go to that link click on enroll now enter the coupon code here and that's it as simple as that how many of you are interested in that you too read the triple angle formula Read it now Tell quickly in the chat box yes or no yes Yes or no in the chat box are we ready for this yes okaylet 's do a task Start your class here I'll give you a homework question okay You are given a homework question all right so let me give you a homework question children Because she's a teacher she 'll give us homework right The teacher will give us homework all right so if you are given save the children Remember this well and I'm giving you homework Write it down for sure tan theta is given to you as 24 over 7 theta belongs to the third quadrant It makes sense tan theta is 24 over 7 Theta belongs to the third quadrant you are given you need to find the value sin 2 theta cos 2 theta and tan 2 theta let me see Who sends me the correct answer okay and if you want We can start tomorrow's class by revising these three by revising this question please make a note okay yes I will definitely catch you all do just that for now Because you people are the ones who should revise it the most Cheke So obviously I would do all of this with you We will also do the triple angle formula But come back and revise it well properly I don't want to overburden you Cheke this is our Vidantoo learning app If you haven't downloaded it yet boss you should do it now You can find many life classes here Free study material is available More than fifty thousand downloads have been made Then go to the Play Store right now Download the work app no way yes Make sure you are doing this work otherwise you will suffer a loss I don't have anything else to say bye guys see you all I'll be back in 12 to 15 with Kramer's rule Class 12 is very important goodbye