Question

Find the general solution:
$cos4x=cos2x$

Answer 1

$\cos 4x=\cos 2x$

$\Rightarrow 2{\cos }^{2}2x-1-\cos 2x=0\Rightarrow \cos 2x=-\frac{1}{2},1$

$\Rightarrow 2x=2n\pi \pm \frac{\pi }{3},2n\pi$

$\Rightarrow x=n\pi \pm \frac{\pi }{6},n\pi$