Hướng dẫn giải :

$\begin{align}  & \cos 9x.\cos 7x-1=\sin 9x.\sin 7x-\sqrt{3}\sin 2x \\ & \Leftrightarrow \cos 7x.\cos 5x+\sin 7x.\sin 5x-\sqrt{3}\sin 2x=1 \\ & \Leftrightarrow \cos 2x-\sqrt{3}\sin 2x=1 \\ & \Leftrightarrow \cos (2x+\frac{\pi }{3})=\cos \frac{\pi }{3} \\ & \Leftrightarrow \left[ \begin{matrix}   2x+\frac{\pi }{3}=\frac{\pi }{3}+k2\pi   \\   2x+\frac{\pi }{3}=\frac{-\pi }{3}+k2\pi   \\\end{matrix} \right.,k\in \mathbb{Z} \\ & \Leftrightarrow \left[ \begin{matrix}   x=k\pi   \\   x=\frac{-\pi }{3}+k\pi   \\\end{matrix} \right.,k\in \mathbb{Z} \\\end{align}$

Chọn C.