Giải phương trình:

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

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

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

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

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