Math Olympiad Problem | Nice Trigonometry Problem | Math Olympiad Training

In this Math Olympiad problem video, we'll tackle a nice Trigonometry Problem to help with your Math Olympiad training. Get ready to challenge your math skills!
#exponential
#exponents
#exponentialproblem
#maths
#mathematics

[@quelquun5633]

One other way to see it is to know that sin^4 -cos^4= sin^2-cos^2. Then everything cancels out and you get the result.

[@SidneiMV]

perfect

[@davidsousaRJ]

I did
f(x) = (cos²x + sin²x.sin²x)/(sin²x + cos²x.cos²x)
= (cos²x + sin²x.(1 - cos²x))/(sin²x + cos²x.(1 - sin²x))
= (cos²x + sin²x - sin²xcos²x))/(sin²x + cos²x - cos²xsin²x))
= (1 - sin²xcos²x)/(1 - sin²xcos²x)
= 1. Very easy.

[@matholympiadonlinesolver]

Nice

[@honestadministrator]

writing z for sin^2 ( x) one gets
f ( x)
= (1 - z + z^2) /( z + ( 1 - z) ^2)
= (1 - z + z^2) /( 1 - z + z^2)
= 1

[@matholympiadonlinesolver]

Nice

[@jwkim4428]

derivative of f(x) is 0. f(x) is constant and f(0)=1.
hence f (x)=1 for all x.

[@matholympiadonlinesolver]

Ok thank you

[@davidsousaRJ]

@jwkim4428 how did you get thsi result? It is very tedious to calculate this derivative by the quotient rule, and there is no obvious term cancellation in the final result.

[@vasilesinescu84]

How do you pronounce x?

[@matholympiadonlinesolver]

What are you hearing?

[@rishabhraj3749]

Bro.. Nice explanation

[@matholympiadonlinesolver]

Thank you