Đáp án:
`x=\frac{\pi}{2}+k\pi` hoặc `x=\frac{\pi}{4}+k\pi`
Giải thích các bước giải:
$\begin{array}{l} (\cos x - \sin x).\sin x\cos x = \cos x.\cos 2x\\ \Leftrightarrow (\cos x - \sin x).\sin x\cos x - \cos x.\cos 2x = 0\\ \Leftrightarrow (\cos x - \sin x).\sin x\cos x - \cos x({\cos ^2}x - {\sin ^2}x) = 0\\ \Leftrightarrow \sin x{\cos ^2}x - {\sin ^2}x\cos x - {\cos ^3}x + {\sin ^2}x\cos x = 0\\ \Leftrightarrow \sin x{\cos ^2}x - {\cos ^3}x = 0\\ \Leftrightarrow {\cos ^2}x(\sin - \cos x) = 0\\ \Leftrightarrow \left[ \begin{array}{l} {\cos ^2}x = 0\\ \sin x - \cos x = 0 \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} \cos x = 0\\ \sin x = \cos x \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} \cos x = 0\\ \tan x = 1 \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} x = \dfrac{\pi }{2} + k\pi \\ x = \dfrac{\pi }{4} + k\pi \end{array} \right. \end{array}$
Vậy `x=\frac{\pi}{2}+k\pi` hoặc `x=\frac{\pi}{4}+k\pi`
