# How do you find the general solutions for 4cos^2 (x) - 3 = 0?

$4 {\cos}^{2} x - 3 = 0$
${\cos}^{2} x = \frac{3}{4}$
$\cos x = \pm \frac{\sqrt{3}}{2}$
$x = \frac{\pi}{3} + k \pi , \frac{2 \pi}{3} + k \pi$
$x = \frac{\pi}{3} \left(1 + 3 k\right) , \frac{\pi}{3} \left(2 + 3 k\right) , k \in \mathbb{Z}$ (i.e. $k$ is an integer)