Answer
$\{0, \frac{2\pi}{3},\frac{4\pi}{3} \}$
Work Step by Step
Step 1. Rewrite the function as
$2(1-cos^2(x))+cos(x)=1$, we have $2cos^2(x)-cos(x)-1=0$
Step 2. Factor the left side to get
$(2cos(x)+1)(cos(x)-1)=0$
Step 3. For $cos(x)=1$, we have $x=0$
Step 4. For $cos(x)=-\frac{1}{2}$, we have $x=\frac{2\pi}{3},\frac{4\pi}{3} $
Step 5. We have the solution set as $\{0, \frac{2\pi}{3},\frac{4\pi}{3} \}$
