Question

giải pt : \(\sqrt{3}\left(2\cos^2x+\cos x-2\right)+\left(3-2\cos x\right)\sin x=0\)

Answer 1

\(\Leftrightarrow\sqrt{3}\left(-2sin^2x+cosx\right)+\left(3-2cosx\right)sinx=0\)

\(\Leftrightarrow-2\sqrt{3}sin^2x+\sqrt{3}cosx+3sinx-2sinx.cosx=0\)

\(\Leftrightarrow\sqrt{3}sinx\left(\sqrt{3}-2sinx\right)+cosx\left(\sqrt{3}-2sinx\right)=0\)

\(\Leftrightarrow\left(\sqrt{3}sinx+cosx\right)\left(\sqrt{3}-2sinx\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{3}sinx+cosx=0\\\sqrt{3}-2sinx=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}sin\left(x+\frac{\pi}{6}\right)=0\\sinx=\frac{\sqrt{3}}{2}\end{matrix}\right.\)