Phương trình $\cos 2x = \cos \left( {x + \frac{\pi }{4}} \right)$ có các nghiệm là:

A. $\left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = - \frac{\pi }{4} + k\frac{{2\pi }}{3}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)$.

B. $\left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = - \frac{\pi }{{12}} + k\frac{{2\pi }}{3}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)$.

C. $\left[ \begin{array}{l}x = - \frac{\pi }{4} + k2\pi \\x = - \frac{\pi }{{12}} + k\frac{{2\pi }}{3}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)$.

D. $\left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = - \frac{\pi }{{12}} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)$.

Đáp án đúng là: B

Ta có $\cos 2x = \cos \left( {x + \frac{\pi }{4}} \right)$

$\Leftrightarrow \left[ \begin{array}{l}2x = x + \frac{\pi }{4} + k2\pi \\2x = - \left( {x + \frac{\pi }{4}} \right) + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)$

$\Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{4} + k2\pi \\x = - \frac{\pi }{{12}} + k\frac{{2\pi }}{3}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)$.