Answer
$\{\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6} \}$
Work Step by Step
Step 1. The equation gives two solutions $cos(x)=-\frac{\sqrt 3}{2}$ and $sin(x)=-\frac{1}{2}$
Step 2. For $cos(x)=-\frac{\sqrt 3}{2}$, we can find all x-values in $[0,2\pi)$ as $x=\frac{5\pi}{6}, \frac{7\pi}{6}$
Step 3. For $sin(x)=-\frac{1}{2}$, we can find all x-values in $[0,2\pi)$ as $x=\frac{7\pi}{6},\frac{11\pi}{6}$
Step 4. The solutions for the original equation in $[0,2\pi)$ are $\{\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6} \}$
