5) $$(2cosx+1)(\sqrt{3}tgx+1)=0$$

Решим уравнение $$(2cosx+1)(\sqrt{3}tgx+1)=0$$. $$2cosx+1 = 0$$ или $$\sqrt{3}tgx+1 = 0$$ 1) $$2cosx+1 = 0$$ $$cosx = -\frac{1}{2}$$ $$x = \pm arccos(-\frac{1}{2}) + 2\pi n, n \in Z$$ $$x = \pm \frac{2\pi}{3} + 2\pi n, n \in Z$$ 2) $$\sqrt{3}tgx+1 = 0$$ $$tgx = -\frac{1}{\sqrt{3}}$$ $$x = arctg(-\frac{1}{\sqrt{3}}) + \pi n, n \in Z$$ $$x = -\frac{\pi}{6} + \pi n, n \in Z$$ Ответ: $$x = \pm \frac{2\pi}{3} + 2\pi n, x = -\frac{\pi}{6} + \pi n, n \in Z$$