Answer
$x=2n\pi$, where $n$ is an integer.
$x=\frac{2\pi}{3}+2n\pi$, where $n$ is an integer.
$x=\frac{4\pi}{3}+2n\pi$, where $n$ is an integer.
Work Step by Step
$cos~2x-cos~x=0$
$cos^2x-sin^2x-cos~x=0$
$cos^2x+cos^2x-1-cos~x=0$
$2~cos^2x-cos~x-1=0$
$cos~x=1$ and $cos~x=-\frac{1}{2}$
The solutions in [0,2π) are:
$x=0$
$x=\frac{2\pi}{3}$
$x=\frac{4\pi}{3}$
General solution:
$x=0+2n\pi=2n\pi$
$x=\frac{2\pi}{3}+2n\pi$
$x=\frac{4\pi}{3}+2n\pi$
where $n$ is an integer.
