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
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:
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.
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
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)
@@iconicsolos1234 Not At All its very Easy for The one who has studied for Olympiads in 9th . I myself did it very easily though I am in 10 just passed 9th in 2023
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
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?
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........
It can be done in an easier way... sin^100(x) + cos^100(x)=1 or, sin^100(x) + cos^100(x)=sin^2(x) + cos^2(x) or, sin^2(x) { 1 - sin^98(x) } + cos^2(x) { 1 - cos^98(x) } = 0 ..... (i) Now, { 1 - sin^98(x) } and { 1 - cos^98(x) } both can be broken down into factors { 1 - sin^2(x) } = cos^2(x) and { 1 - cos^2(x) } = sin^2(x) respectively using the formula (a^n-b^n). Therefore in (i) we can take sin^2(x) and cos^2(x) common and equate them to zero... Hence you'll get the solution.
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.
Bro from powering 1st eqn (by you) by 50 both side then we get sin ⁵⁰⁰⁰(x)=cos ¹⁰⁰ (x) and solving it with your 2nd eqn it is only possible when sin(x) =1 or 0 or -1. The same sir did with his way of solving.
Sin^100 x + cos^100 x Taking log on both sides Log(sin^100 x ) + log(cos^100 x) = log(1] 100log(sinx) + 100log(cosx)=0 Log(sinx) = -log(cosx) Sinx= - cosx X= 135 degree Checking Sin135 = 1/sqrt 2 Cos135=-1/sqrt 2 Adding both with power of 100 which is even we get 1/2 +1/2=1
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)
Ye kya hota h bhai
our problem solving criteria got improve by solving your amazing questions ❤❤❤❤
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
He is the most underrated teacher a legend of iit jee maths on TH-cam 😢
Mata pita aur guru se padkar es duniya me koi nhi 🙏🙏🙏 love you guruji ♥️♥️♥️
Badkar bhai
@@Kingboyprince45😂😂
Bhai badhkar hota hai padhkar nhi
@@HARSHSHARMA-db9oh chutiye Mt sikha hme
Jis aapne ye seekh lia ki sikhte kaise hai uss din aap life me kuch bhi kar skte hai.........lines❤️❤️❤️❤️❤️❤️❤️❣️❣️❣️❣️❣️
Amazing sir
Keep coming with these types of wonderstruckers !!!
Masha' Allah ♥sir. Aap kitne achi tarah samjhate hai
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:
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.
Log (sinx + cosx) ≠ log (sinx ⋅ cosx)
Learnt new method of solving..Thank u sir
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
This was so beautiful and amazing concept ❤❤❤.
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
Amazing style , very cool teaching
dekhte hi kr diya sir 🙏
Kya batya hai sir apna Dil sa sukriya❤❤❤❤
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)
Power high means satisfy and put values comparing sinx+cosx=1,right sir...
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
good evening sir... i like your videos very much
Aman sir by trial error method it can come pi/2 directly
Sir ek dam bhannat lagti hai 🥰🥰
Well this was a 10th grade question with some basic concept of 11th
Pucha kisine pucha
Nope it is difficult for a 10th grade student
@@omsharma977 bhai toh tujhse kisne pucha reply krne don't make this meme boring by using it everywhere.
Preserve it. It's a gem.❤
@@iconicsolos1234 Not At All its very Easy for The one who has studied for Olympiads in 9th . I myself did it very easily though I am in 10 just passed 9th in 2023
Puchaaaa kisine.? Puchaa kisine?! Kisine nhi puchaa!
By Aman dhatarwal
Great work by great personality 👏👌
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?
Love you sir❣️❣️
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
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.
Sir can we differentiate both sides wrt x which will give us cotx=cot⁹⁹x from which we can easily solve?
Thank you so much sir ❤️
Not for Jee mathematics can be someone's main subject also... Thank you sir
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?
You have to raise them to the hundredth power too,so sin^100(π)=0 and cos^100(π)=1 so 1+0=1
-1 ki power 100 +1 hoti hai
Solved it within 30 secs 😆
Sir I like your teaching way and your concepts.
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........
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
It can be done in an easier way...
sin^100(x) + cos^100(x)=1
or, sin^100(x) + cos^100(x)=sin^2(x) + cos^2(x)
or, sin^2(x) { 1 - sin^98(x) } + cos^2(x) { 1 - cos^98(x) } = 0 ..... (i)
Now, { 1 - sin^98(x) } and { 1 - cos^98(x) } both can be broken down into factors { 1 - sin^2(x) } = cos^2(x) and { 1 - cos^2(x) } = sin^2(x) respectively using the formula (a^n-b^n).
Therefore in (i) we can take sin^2(x) and cos^2(x) common and equate them to zero... Hence you'll get the solution.
Can someone tell the name of background music of intro plzzzzzz
Very nice sir. Lot of learnings in one question. Keep it up Sir ❤❤
Bahut badhiya video hai
We can also do this by graph observation 😊
integral of f(x) = f(x) then f(x)=? f(x) is not e power x. please tell sir
Can X be either 0° or 90° ?
Tell me ..
Diffretiatial form se seedha solved!
Extended form of Tittus lemma and Rms› Am😊
Best math teacher of all time
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
Sir kya aap ioqm ke content post karoge
Sir aap ke sabhi saval men naya chij sikhane ko Milta Hai
Great sir ji. Keep it up
Sir aap konsa application me online course padha rhe hai.
Complex no se aisa koi paira saoal laiye sir, please 🙏
Splendid explanation sir! Yeh dil mange more!
Can we do this by taking example of angle X'
Love from Bangladesh 🇧🇩
Sir, why did you consider pi by 2 only?
Because pie by 2 = 90 ⁰
sir hit and trial se bhi ho jaega
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.
is n in power?
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
sir please launch your maths cource for jee 2024
Thanks a lot Sir ❤
Sir x=Π/4 bhi ho sakta hai.
Sir Aap Bsc ki maths prasandhaiye please
sir colagge ka maths ke uper bhi vedioes bno
Sin^n x + Cos^n x = 1 - n/2 Sin^2 xCos^2x This is the simple solution to this question.
where n is even number
kaise
@@bhagyeshbetha8321 sin^4x+cos^4x = 1-2sin^2xcos^2x
Sir bahut achhe lagti hai aapki video
Sir doubt: What if sin^100 x = cos^2 x and cos^100 x = sin^2 x? Won't we have to consider those possibilities also?
only x=nπ/2 will satisfy both equations which u gave
Please clear this doubt sir ji
Bro from powering 1st eqn (by you) by 50 both side then we get sin ⁵⁰⁰⁰(x)=cos ¹⁰⁰ (x) and solving it with your 2nd eqn it is only possible when sin(x) =1 or 0 or -1.
The same sir did with his way of solving.
Thanks sir ❤
Tumse yah saval solve hua
@@Ganesh2168Xvjti nahi hua par mene try Kiya
Me 10th standard ka student hu mene apna trigo ke knowledge ko apply karne ki koshish ki ...:)
Me 11th me hu
@@mrunal1099 i am also in 10th giving math board on 21 march.
Sir bahut kuchh sikhne ko milta hai aapki video me ❤
Sir , when X=0,90 satisfying this question
Excellent
Sir x=45 ho sakta hai kya
Sir maza aa gaya 🪄🙌🏻🙏🏻
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)😢
Correct hai aap π/2=90° hi hota hai
Gazab lagte hne sir
Really interesting questions
Absolutely awesome explanation.
Amazing question.
Sir you just awesome
Sir ek line me solve hoga.itna lengthy kyun.
Sir x= 0 kyo include hoga ,,, ussse 1 kaise aayega?????
Lekin value 0 toh ayega na. Woh bhi toh ek legit soln hai.
Woah i just solved them by looking at it 🎉
Sir maths Mera thoda weak hai improve kaise kare
Bahut hi basics se karwaya jayega
it can be solved using graph much easy approach
Why sir is so underrated 😔
You are my inspiration
Apke sabhi videos dekta hu
Without seeing answer is n ×pi /2
Where n is a whole number
Thank you sir
Sir you are great
This is basic 10th question
Where x=0 or 90
Great sir
It is quite evident from the sum that - sin x = 1 , cos(x) = 0 or vice versa.
In the last for cos it has become quite ambiguous
Sin^100 x + cos^100 x
Taking log on both sides
Log(sin^100 x ) + log(cos^100 x) = log(1]
100log(sinx) + 100log(cosx)=0
Log(sinx) = -log(cosx)
Sinx= - cosx
X= 135 degree
Checking
Sin135 = 1/sqrt 2
Cos135=-1/sqrt 2
Adding both with power of 100 which is even we get 1/2 +1/2=1
Galat ha, logarithm aise kaam nhi karta
@@KSM94K kya galalt hai batao?
Pls
@@varun8762 log(a+b)≠loga+logb
It's not true for every case
@@KSM94K ok thx i missed it
@@KSM94Klog(a×b)= loga+logb hota tha
Aapki bhannat wali dailok mast lagti hai
nπ is an answer as well
Mushe aap bta do aapne sikh kar kya kiya kitne billion dolller ki company start ki
Sin²⁰⁰ + Cos²⁰⁰ = 1
Sir please solve
My school teacher gave me this
I'm not able to solve
❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
Good explanation
I knew the general graph of sinⁿx + cosⁿx, so solved it using graph.
same concept question in jee mains
Sin⁷x + cos⁷x tha usme