Lời giải của Tự Học 365

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

Đáp án cần chọn là: b