Тип 15 № 13845

Упростим уравнение: $$2\sin^2x + \sqrt{3}\cos x - 2 = 0$$ Выразим $\sin^2x$ через $\cos x$: $$2(1 - \cos^2x) + \sqrt{3}\cos x - 2 = 0$$ $$-2\cos^2x + \sqrt{3}\cos x = 0$$ $$\cos x(-2\cos x + \sqrt{3}) = 0$$ $$\left[ \begin{aligned} &\cos x = 0 \\ &\cos x = \frac{\sqrt{3}}{2} \end{aligned} \right. \Rightarrow \left[ \begin{aligned} &x = \frac{\pi}{2} + \pi k \\ &x = \pm\frac{\pi}{6} + 2\pi k \end{aligned} \right., \quad k \in \mathbb{Z}$$