Question

Sin^4x+cos^4x = cos4x

Answer 1

$\sin ^4x+\cos^4x=\cos4x\\ \sin^4x+2\cos^2x\sin^2x+\cos^4x-2\cos^2x\sin^2x=\cos 4x\\ (\sin^2x+\cos^2x)^2-0.5\sin^22x=1-2\sin^22x\\ 1-0.5\sin^22x=1-2\sin^22x\\ 1.5\sin^22x=0\\ \sin2x=0\\ 2x=\pi k,k \in \mathbb{Z}\\ \\ \boxed{x=\frac{\pi k}{2},k \in \mathbb{Z}}$