Hướng dẫn giải:

Ta có (*) \( \Leftrightarrow (2\cos x-1)(2\sin x+\cos x)=\sin x(2\cos x-1) \)

 \( \Leftrightarrow (2\cos x-1)\left[ (2\sin x+\cos x)-\sin x \right]=0\Leftrightarrow (2\cos x-1)(\sin x+\cos x)=0 \)

\(\Leftrightarrow \left[ \begin{align}  & \cos x=\frac{1}{2} \\  & \sin x=-\cos x \\ \end{align} \right.\)\(\Leftrightarrow \left[ \begin{align} & \cos x=\cos \frac{\pi }{3} \\  & \tan x=-1=\tan \left( -\frac{\pi }{4} \right) \\ \end{align} \right.\)\(\Leftrightarrow \left[ \begin{align}  & x=\pm \frac{\pi }{3}=k2\pi  \\  & x=-\frac{\pi }{4}+k\pi  \\ \end{align} \right.\text{ }(k\in \mathbb{Z})\).