[tex]$\sqrt{3}\sin x\cos x-\cos^2x=0\Leftrightarrow \cos x\left ( \sqrt{3}\sin x-\cos x \right )=0\\$[/tex]

[tex]$\cos x\left ( \frac{\sqrt{3}}{2}\sin x-\frac{1}{2}\cos x \right )=0\Leftrightarrow \cos x\left ( \cos \frac{\pi}{6}\sin x-\sin \frac{\pi}{6}\cos x \right )=0\\$[/tex]

[tex]$\cos x\sin \left ( \frac{\pi}{6}-x \right )=0\Rightarrow \left[ \begin{gathered} \cos x =0\\\sin \left ( \frac{\pi}{6}-x \right )=0 \end{gathered} \right.\Rightarrow \left[ \begin{gathered} x=\frac{3\pi}{2}+\pi k\\x=\frac{7\pi}{6}+\pi k \end{gathered} \right.,k\in \mathbb{Z}$[/tex]