Important problem of Trigonometry | General Solution Of sin^100 x + cos^100 x = 1

In today's video, let's find the solution to an interesting trigonometric problem.
We have to solve sin^100 x + cos^100 x = 1
So we need to find the value of x for which the above expression will be true.
We already know that sin^2 x + cos^2 x = 1. This identity will be of great use for solving this expression.
Let's see how we can solve this and understand some very useful properties of trigonometry.
Trigonometry problems | Important trigonometry questions | Trigonometry expressions | Trigonometry JEE problems | Trigonometry for IIT JEE | Trigonometry questions for IIT JEE
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[@_AmanKumar2592AA]

Successive differentiation formula hai yeah 👍
Sin(ax + b) = a^n sin(ax + b+ nπ/2)
Cos(ax +b ) = a^n Cos(ax + b + nπ/2)

[@Mfers_allover]

Amazing sir
Keep coming with these types of wonderstruckers !!!

[@pranjalpandey972]

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[@mathq123]

Great work by great personality 👏👌

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Amazing style , very cool teaching

[@Lifechangingmotivational-tk5go]

Mata pita aur guru se padkar es duniya me koi nhi 🙏🙏🙏 love you guruji ♥️♥️♥️

[@princekumaryadavofficial3984]

Badkar bhai

[@Indiandragon]

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[@HARSHSHARMA-db9oh]

Bhai badhkar hota hai padhkar nhi

[@Lifechangingmotivational-tk5go]

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[@bhavesh0295]

This was so beautiful and amazing concept ❤❤❤.

[@yashbhitre8235]

U r doing a great effort sir,I bet u are submerged in every seriously studying iit jee aspirant, because tough questions is the only need at this time (along with sol.) And thnk u sir for your kind act

[@pranavmohta5629]

He is the most underrated teacher a legend of iit jee maths on CZcams 😢

[@kuchipoo2057]

Learnt new method of solving..Thank u sir

[@mohan153doshi]

Absolutely awesome explanation.

[@anilkumarbandyopadhyay5235]

Splendid explanation sir! Yeh dil mange more!

[@divyanjalisharma7088]

Jis aapne ye seekh lia ki sikhte kaise hai uss din aap life me kuch bhi kar skte hai.........lines❤️❤️❤️❤️❤️❤️❤️❣️❣️❣️❣️❣️

[@KoushikDas2005]

Thanks a lot Sir ❤

[@gamingwithpriyanshu577]

Kya batya hai sir apna Dil sa sukriya❤❤❤❤

[@maheshvyas5492]

Great sir ji. Keep it up

[@AmitKumar-us6is]

good evening sir... i like your videos very much

[@rohitbharti1183]

Sir I like your teaching way and your concepts.

[@AKBARCLASSES]

Thank you so much sir ❤️

[@manashidevbarman-jx8rn]

Amazing question.

[@QwertyUiop-ux2yh]

Sir taking log on both sides we get
100*log(sinx.cox)=0
=> sinx.cosx =1
=> sin(2x) = 2
But this is not possible , nevertheless we are still getting the ans as 0,π÷2, etc . How?
Please reply.

[@MokshitArora.]

Log (sinx + cosx) ≠ log (sinx ⋅ cosx)

[@amitkumardas6703]

Power high means satisfy and put values comparing sinx+cosx=1,right sir...

[@upendrakumarsingh4301]

Very nice sir. Lot of learnings in one question. Keep it up Sir ❤❤

[@vijay-music-jnv]

Sir bahut kuchh sikhne ko milta hai aapki video me ❤

[@AyushGupta-rq4qu]

Masha' Allah ♥sir. Aap kitne achi tarah samjhate hai

[@hackwithtechnoboy548]

dekhte hi kr diya sir 🙏

[@MOHITKUMAR-ft1nr]

You are my inspiration

[@honestadministrator]

Writing y for sun^2 (x) one gets
y^n + (1-y)^n = 1
y = 0, 1 are trivial solutions .
i.e. x lies either of coordinate axis

[@RAJANKUMAR-mb2xw]

Really interesting questions

[@Akpvin]

Great sir

[@letsexplore5262]

Love you sir❣️❣️

[@muskuraiye79]

Sir you are great

[@arman_singh...]

Solved it within 30 secs 😆

[@vijay-music-jnv]

Sir bahut achhe lagti hai aapki video

[@kailashkushwaha9296]

Sir you just awesome

[@ShubhamTivarekar]

Thank you sir

[@srijonsinchanganguly2779]

Not for Jee mathematics can be someone's main subject also... Thank you sir

[@divyeshranwa4957]

Sir एक request है jee mains 2021 मै quadratic का ques आया था उसका solution samjha dijiye sir plz
The number of pairs (a, b) of real numbrs, such that whenever a is root of the equation x ^ 2 +ax+b=0, alpha^2-2 is also a root of this equation, is:

[@mathmagic8577]

Bahut badhiya video hai

[@aysmn7449]

Sir can we differentiate both sides wrt x which will give us cotx=cot⁹⁹x from which we can easily solve?

[@als2cents679]

Beauty of this question is that it works with power 1 as well, e.g.
sin(x) + cos(x) = 1
will also have same solution.
Yeh question hona chahiye thaa
sin^100(x) + cos^100(x) = sin(x) + cos(x)

[@binaykumar2292]

Sir aap konsa application me online course padha rhe hai.

[@user-qr3pl5lu3y]

Excellent

[@siddharthjain-vh6ub]

Waise toh mujhe shuru ke 4 steps samj aaye kyoki mai 10th passed hu par
Mera ek swaal h ki x = 90 degrees bhi toh ho sakta h (please hasna mat koi)😢

[@MathematicalPool]

Correct hai aap π/2=90° hi hota hai

[@AgentGaming-bx4sk]

Aman sir by trial error method it can come pi/2 directly

[@mr.allroundergautam8147]

Hi can anyone prove or disprove;
(Sin^2n x+ Cos ^2n x) = 1- n sin^2x cos^2 x.For all integers which are either greater than or equal to 2.I had find this expression correct for integers 2,3 and 100.

[@corporalgaming8786]

Sir is ma power 50 ko whole common la kar sin^2x+cos^2 ko 1 karka 1power50 sa 1 ka barabar nahi kar sakta?

[@bindurai5942]

Thank you so much aapko bhi aur Lega sir ko bhi.
Aap dono se hi padhke aaj mere boards me 75/80 aa rahe hai.
Boht boht shukriya sir.

[@mithileshkumar9236]

Sir aap ke sabhi saval men naya chij sikhane ko Milta Hai

[@harshgupta351]

Sir isme x=π/4 and intergral multiples of it bhi satisfy kar rahe h jo ki general soln ka part nhi h. ye values kese aa rahi h

[@atharvbhadri2676]

Best math teacher of all time

[@thenaturesgarden7961]

Can we do this by taking example of angle X'

[@saikiranabburi1802]

Sir can you make a video about how can we find the area of shades region of any diagram pl sir will you send it

[@MOHITKUMAR-ft1nr]

I love you sir❤❤

[@sunilsaini-rd9es]

sir hit and trial se bhi ho jaega

[@ujjwalghosh389]

Sir ek dam bhannat lagti hai 🥰🥰

[@shivangsingh2463]

Sir maza aa gaya 🪄🙌🏻🙏🏻

[@creative_philomath]

Can X be either 0° or 90° ?
Tell me ..

[@bhaskarkhandewal3257]

Solved simpler cases for solving this equation and got intuition that answers of this equation are same as those of sin²xcos²x=0. You can verify that yourself

[@scarfallBENGALI]

🙏🏻

[@AmanGupta-fi4wb]

Sir kya aap ioqm ke content post karoge

[@haasanbismil8723]

Gazab lagte hne sir

[@saraswathi4123]

integral of f(x) = f(x) then f(x)=? f(x) is not e power x. please tell sir

[@surajdeopa6922]

sir please launch your maths cource for jee 2024

[@Brid727]

Sir I think there are 4 answers, 2n*pi, pi/2 + 2n*pi, pi + 2n*pi, 3*pi/2 + 2n*pi, where n is an integer

[@thepi553]

How to find the height of any triangle when side length is given. I mean that if any triangle's side is a, b and c then what will the height be of this triangle.............🤔. Is there any formula, by using that we can find the height of any triangle........

[@Mitesh_Yadav]

Yes , 1st find the area using heron's formula and then equate this with 1/2 ×bh where b can be any of the sides a,b,c

[@somnathchattopadhyay1596]

I'm not a student but will retire from engineering service next year. I love your video and refresh my love for mathematics even after so many years . Thank you

[@bikramchakraborty9999]

Complex no se aisa koi paira saoal laiye sir, please 🙏

[@shouryasingh1422]

wow

[@FutureWaitHim]

Diffretiatial form se seedha solved!
Extended form of Tittus lemma and Rms› Am😊

[@adityaparikh55]

I think x = nπ/2 doesn't work because at π cos x is -1 and sin is 0, (-1)+0=-1. The only values that would give the sum as 1 would be 2nπ or 2nπ+(π/2). I'm not sure can someone clarify this?

[@SMD2005]

You have to raise them to the hundredth power too,so sin^100(π)=0 and cos^100(π)=1 so 1+0=1

[@zigzag3720]

-1 ki power 100 +1 hoti hai

[@DUaspirant-nv1ek]

Love from Bangladesh 🇧🇩

[@MOHITKUMAR-ft1nr]

Aapki bhannat wali dailok mast lagti hai

[@sirajzama8080]

Woah i just solved them by looking at it 🎉

[@vrajesh.k]

sir colagge ka maths ke uper bhi vedioes bno

[@MOHITKUMAR-ft1nr]

Apke sabhi videos dekta hu

[@lakshya5946]

I'm Not Sure why I found Sir a bit worried in this video?
Positive Vibes and Wishes from me

[@mrunal1099]

Thanks sir ❤

[@DOGLAPAN3015]

Tumse yah saval solve hua

[@mrunal1099]

@@DOGLAPAN3015 nahi hua par mene try Kiya
Me 10th standard ka student hu mene apna trigo ke knowledge ko apply karne ki koshish ki ...:)

[@DOGLAPAN3015]

Me 11th me hu

[@studymaster7388]

​@@mrunal1099 i am also in 10th giving math board on 21 march.

[@Indianfootballstrike]

❤

[@Dhanika112]

thank u sir , aap nhot acha content dete h

[@garvitsingla5386]

Can someone tell the name of background music of intro plzzzzzz

[@princearya5987]

Why sir is so underrated 😔

[@ArjunIITB.]

I knew the general graph of sinⁿx + cosⁿx, so solved it using graph.

[@Acharya240]

Sin²⁰⁰ + Cos²⁰⁰ = 1
Sir please solve
My school teacher gave me this
I'm not able to solve

[@hemlatarathore9722]

x=90

[@irl.escaper]

In the last for cos it has become quite ambiguous

[@Physicslover1199]

❤❤❤❤🎉

[@user-km5zt2cj3o]

Sir x=Π/4 bhi ho sakta hai.

[@Huntergaming-uq6hz]

Sir x=45 ho sakta hai kya

[@ssuma2645]

Sir, why did you consider pi by 2 only?

[@akedit196]

Because pie by 2 = 90 ⁰

[@lalikantkumar-vz9cm]

Sir Aap Bsc ki maths prasandhaiye please

[@gurshanbajwa6408]

This is basic 10th question
Where x=0 or 90

[@choudharylekhrajbhicher152]

Sir , when X=0,90 satisfying this question

[@AbhishekRaj-ho3ii]

Very tricky

[@shouryagupta7785]

nπ is an answer as well

[@arshealamkhan7743]

Maine jab jee mains di thi tab aisa hi question aaya tha

[@hemant.564]

Sir we love 💕 ite

[@arulbiswas1260]

It is quite evident from the sum that - sin x = 1 , cos(x) = 0 or vice versa.

[@harshitrathore439]

FIRST QUESTION THAT I WAS ABLE TO OLVE MY SELF

[@AmitKumarSingh-op2cx]

Without seeing answer is n ×pi /2
Where n is a whole number

[@armanrai3832]

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Good explanation