Question

Cos2x+cos4x+cos(П-3x)=0

Answer 1

$cos2x+cos4x=2cos3xcosx\\cos(\pi-3x)=-cos3x\\2cos3xcosx-cos3x=0\\cos3x(2cosx-1)=0\\1) cos3x=0, 3x=\frac{\pi}{2}+\pi n, x=\frac{\pi }{6}+\frac{\pi n}{3}, n\in Z\\2)2cosx-1=0, cosx=\frac{1}{2}\\x=\pm \frac{\pi}{3}+2\pi k,k\in Z$