5. (1 балл) Решить уравнение 2cos(x+π/3)=1.

$$2 \cos(x+\frac{\pi}{3}) = 1$$

$$\cos(x+\frac{\pi}{3}) = \frac{1}{2}$$

$$x+\frac{\pi}{3} = \pm \arccos(\frac{1}{2}) + 2\pi n, n \in \mathbb{Z}$$

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

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

1) $$x = -\frac{\pi}{3} + \frac{\pi}{3} + 2\pi n = 2\pi n, n \in \mathbb{Z}$$

2) $$x = -\frac{\pi}{3} - \frac{\pi}{3} + 2\pi n = -\frac{2\pi}{3} + 2\pi n, n \in \mathbb{Z}$$

Ответ: $$x = 2\pi n$$, $$x = -\frac{2\pi}{3} + 2\pi n, n \in \mathbb{Z}$$