(2cosx+1) (√3 tgx+1)=0

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