Question

Sin^4 x + cos^4 = cos^2 2x

Answer 1

$\sin^4x+\cos^4x=\cos^22x\\ \\ \sin^4x+\cos^4x=(\cos^2x-\sin^2x)^2\\ \\ \sin^4x+\cos^4x=\cos^4x+\sin^4x-2\sin ^2x\cos^2x\\ \\ 0.5\sin^22x=0\\ \\ \sin2x=0\\ \\ x= \frac{\pi k}{2},k\in \mathbb{Z}$