\(\Leftrightarrow2\sqrt{3}sinx.cosx+2cos^2x-1=2cosx-1\)
\(\Leftrightarrow cosx\left(\sqrt{3}sinx+cosx-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\Rightarrow x=\frac{\pi}{2}+k\pi\\\sqrt{3}sinx+cosx=1\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow\frac{\sqrt{3}}{2}sinx+\frac{1}{2}cosx=\frac{1}{2}\)
\(\Leftrightarrow sin\left(x+\frac{\pi}{6}\right)=\frac{1}{2}=sin\left(\frac{\pi}{6}\right)\)
\(\Rightarrow\left[{}\begin{matrix}x+\frac{\pi}{6}=\frac{\pi}{6}+k2\pi\\x+\frac{\pi}{6}=\frac{5\pi}{6}+k2\pi\end{matrix}\right.\) \(\Rightarrow...\)
