Answer
$x=\frac{2\pi}{3}+2n\pi$ and $x=\frac{4\pi}{3}+2n\pi$, where $n$ is an integer.
Work Step by Step
$cos~x+1=-cos~x$
$2~cos~x=-1$
$cos~x=-\frac{1}{2}$
The period of $cos~x$ is $2\pi$. The solutions in the interval: $[0,2\pi)$ are:
$x=\frac{2\pi}{3}$ and $x=\frac{4\pi}{3}$
Now, add multiples of $2\pi$ to each of the solutions:
$x=\frac{2\pi}{3}+2n\pi$ and $x=\frac{4\pi}{3}+2n\pi$, where $n$ is an integer.
