Showing posts with label squared term on LHS. Show all posts
Showing posts with label squared term on LHS. Show all posts

Friday, May 22, 2015

Mock Olympiad Math Problem: Solve $\large 3^{\sin^4 x-\cos^2 x}-3^{\cos^4 x-\sin^2 x}=\cos 2x$.

Solve $\large 3^{\sin^4 x-\cos^2 x}-3^{\cos^4 x-\sin^2 x}=\cos 2x$.

$\large 3^{\sin^4 x-\cos^2 x}-3^{\cos^4 x-\sin^2 x}=\cos 2x$

$\large 3^{\sin^4 x-\cos^2 x}\left(1-\dfrac{3^{\cos^4 x-\sin^2 x}}{3^{\sin^4 x-\cos^2 x}}\right)=\cos 2x$