$1-2\cos 2x-\sqrt{3}\sin x+\cos x=0$
$\Leftrightarrow \sin^{2}x+\cos^{2}x-2(\cos^{2} x-\sin^{2} x)-\sqrt{3}\sin x+\cos x=0$
$\Leftrightarrow 3\sin^{2} x-\cos^{2} x-(\sqrt{3}\sin x-\cos x)=0$
$\Leftrightarrow (\sqrt{3}\sin x-\cos x)(\sqrt{3}\sin x+\cos x)-(\sqrt{3}\sin x-\cos x)=0$
$\Leftrightarrow (\sqrt{3}\sin x-\cos x)(\sqrt{3}\sin x+\cos x-1)=0$
Tới đây giải bình thường. ^^