a)Phương trình tương đương với: $2\cos^2x+2\sqrt3\sin x\cos x=\cos x-\sqrt3\sin x$$\Leftrightarrow \frac{1}{2}\cos2x+\frac{\sqrt3}{2}\sin2x=\frac{1}{2}\cos x-\frac{\sqrt3}{2}\sin x$$\Leftrightarrow \cos\left(2x-\frac{\pi}{3}\right)=\cos\left(x+\frac{\pi}{3}\right)$$\Leftrightarrow \left[ \begin{array}{l} 2x-\frac{\pi}{3}=x+\frac{\pi}{3}+k2\pi\\2x-\frac{\pi}{3}=-x-\frac{\pi}{3}+k2\pi \end{array} \right.,k\in\mathbb{Z}$$\Leftrightarrow \left[ \begin{array}{l} x=\frac{2\pi}{3}+k2\pi\\x=\frac{k2\pi}{3} \end{array} \right.,k\in\mathbb{Z} \Leftrightarrow x=\frac{k2\pi}{3},k\in\mathbb{Z}$
a)Phương trình tương đương với: $2\cos^2x
-1+2\sqrt3\sin x\cos x=\cos x-\sqrt3\sin x$$\Leftrightarrow \frac{1}{2}\cos2x+\frac{\sqrt3}{2}\sin2x=\frac{1}{2}\cos x-\frac{\sqrt3}{2}\sin x$$\Leftrightarrow \cos\left(2x-\frac{\pi}{3}\right)=\cos\left(x+\frac{\pi}{3}\right)$$\Leftrightarrow \left[ \begin{array}{l} 2x-\frac{\pi}{3}=x+\frac{\pi}{3}+k2\pi\\2x-\frac{\pi}{3}=-x-\frac{\pi}{3}+k2\pi \end{array} \right.,k\in\mathbb{Z}$$\Leftrightarrow \left[ \begin{array}{l} x=\frac{2\pi}{3}+k2\pi\\x=\frac{k2\pi}{3} \end{array} \right.,k\in\mathbb{Z} \Leftrightarrow x=\frac{k2\pi}{3},k\in\mathbb{Z}$