Answer
The solution set is:
$\{\frac{5\pi}{12}, \frac{7\pi}{12}, \frac{17\pi}{12}, \frac{19\pi}{12}\}$
Work Step by Step
$-2~cos~2x = \sqrt{3}$
$cos~2x = -\frac{\sqrt{3}}{2}$
$2x = arccos(-\frac{\sqrt{3}}{2})$
$2x = \frac{5\pi}{6}, \frac{7\pi}{6}, \frac{17\pi}{6}, \frac{19\pi}{6}$
$x = \frac{5\pi}{12}, \frac{7\pi}{12}, \frac{17\pi}{12}, \frac{19\pi}{12}$
For the domain $[0, 2\pi]$, the solution set is:
$\{\frac{5\pi}{12}, \frac{7\pi}{12}, \frac{17\pi}{12}, \frac{19\pi}{12}\}$
