Решите: √3cos+2sinxcosx=0

[latex]\sqrt3\cos x+2\sin x\cos x=0\\\cos x(\sqrt3+2\sin x)=0\\\begin{cases}\cos x=0\\\sqrt3+2\sin x=0\end{cases}\Rightarrow \begin{cases}\cos x=0\\\sin x=-\frac{\sqrt3}2\end{cases}\Rightarrow\begin{cases}x=\frac\pi2+\pi n\\x=(-1)^n\cdot\frac{7\pi}6+\pi n\end{cases}[/latex]