Answer
$x=\dfrac{\pi}{3}, \dfrac{2 \pi}{3}, \dfrac{4 \pi}{3}, \dfrac{ 5\pi}{3}$
Work Step by Step
Use the identity double angle formula: $ 2 \cos^2 x-1=-2 \cos^2 x$
Then, we have
$4 \cos^2 x-1 =0$
$\implies \cos^2 x=\dfrac{1}{4}$
Here, $\cos x=\dfrac{1}{2}$ and $\cos x=- \dfrac{1}{2}$
Thus, we have $x=\dfrac{\pi}{3}, \dfrac{2 \pi}{3}, \dfrac{4 \pi}{3}, \dfrac{ 5\pi}{3}$
