4) 2 cos(x/3) = √3

Решение: $$2 cos(\frac{x}{3}) = \sqrt{3}$$ $$cos(\frac{x}{3}) = \frac{\sqrt{3}}{2}$$ $$\frac{x}{3} = \pm \arccos(\frac{\sqrt{3}}{2}) + 2\pi k, k \in \mathbb{Z}$$ $$\frac{x}{3} = \pm \frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$$ $$x = \pm \frac{\pi}{2} + 6\pi k, k \in \mathbb{Z}$$ Ответ: $$x = \pm \frac{\pi}{2} + 6\pi k, k \in \mathbb{Z}$$