31. 6 (2 cos x - √3) (cos 3x -√3/2) = 0.

1) $$2cos x - \sqrt{3} = 0$$

$$cos x = \frac{\sqrt{3}}{2}$$

$$x = \pm \frac{\pi}{6} + 2\pi n, n \in Z$$

2) $$cos 3x - \frac{\sqrt{3}}{2} = 0$$

$$cos 3x = \frac{\sqrt{3}}{2}$$

$$3x = \pm \frac{\pi}{6} + 2\pi n, n \in Z$$

$$x = \pm \frac{\pi}{18} + \frac{2\pi n}{3}, n \in Z$$

Ответ: $$x = \pm \frac{\pi}{6} + 2\pi n, x = \pm \frac{\pi}{18} + \frac{2\pi n}{3}, n \in Z$$