Art of Problem Solving

Euc20198/Sub-Problem 2: Difference between revisions

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== Problem ==
== Problem ==


Given <math>0<x<\frac{\pi}{2}</math>, cos(3/2cos(x)) = sin(3/2sin(x)), determine sin(2x), represented in the form (a(<math>\pi</math>)^2 + b(<math>\pi</math>) + c)/d where a,b,c,d are integers
Given <math>0<x<\frac{\pi}{2}</math> and <math>\cos(\frac{3}{2}\cos(x))</math> = <math>\sin(\frac{3}{2}\sin(x))</math>, determine <math>\sin(2x)</math>, represented in the form (a(<math>\pi</math>)^2 + b(<math>\pi</math>) + c)/d where a, b, c, d are integers.


== Solution ==
== Solution ==

Revision as of 15:23, 12 October 2025

Problem

Given $0<x<\frac{\pi}{2}$ and $\cos(\frac{3}{2}\cos(x))$ = $\sin(\frac{3}{2}\sin(x))$, determine $\sin(2x)$, represented in the form (a($\pi$)^2 + b($\pi$) + c)/d where a, b, c, d are integers.

Solution

Video Solution

https://www.youtube.com/watch?v=3ImnLWRcjYQ

~NAMCG