Answer
Solutions:
$x=0$
$x=\frac{\pi}{8}$
$x=\frac{3\pi}{8}$
$x=\frac{5\pi}{8}$
$x=\frac{7\pi}{8}$
$x=\frac{9\pi}{8}$
$x=\frac{11\pi}{8}$
$x=\frac{13\pi}{8}$
$x=\frac{15\pi}{8}$
Work Step by Step
$cos~4x(cos~x-1)=0$
$cos~4x=0$ or $cos~x=1$
$cos~4x=0$
$4x=\frac{\pi}{2}$
$x=\frac{\pi}{8}$
$4x=\frac{3\pi}{2}$
$x=\frac{3\pi}{8}$
$4x=\frac{5\pi}{2}$
$x=\frac{5\pi}{8}$
$4x=\frac{7\pi}{2}$
$x=\frac{7\pi}{8}$
$4x=\frac{9\pi}{2}$
$x=\frac{9\pi}{8}$
$4x=\frac{11\pi}{2}$
$x=\frac{11\pi}{8}$
$4x=\frac{13\pi}{2}$
$x=\frac{13\pi}{8}$
$4x=\frac{15\pi}{2}$
$x=\frac{15\pi}{8}$
$cos~x=1$
$x=0$
