Giải phương trình:

\(\cos \left( {2x + \frac{\pi }{5}} \right) = \frac{{\sqrt 2 }}{2}\);

Do \(\cos \frac{\pi }{4} = \frac{{\sqrt 2 }}{2}\) nên \(\cos \left( {2x + \frac{\pi }{5}} \right) = \frac{{\sqrt 2 }}{2}\) \( \Leftrightarrow \cos \left( {2x + \frac{\pi }{5}} \right) = \cos \frac{\pi }{4}\)

\( \Leftrightarrow \left[ \begin{array}{l}2x + \frac{\pi }{5} = \frac{\pi }{4} + k2\pi \\2x + \frac{\pi }{5} = - \frac{\pi }{4} + k2\pi \end{array} \right.\,\left( {k \in \mathbb{Z}} \right)\)

\( \Leftrightarrow \left[ \begin{array}{l}2x = \frac{\pi }{{20}} + k2\pi \\2x = - \frac{{9\pi }}{{20}} + k2\pi \end{array} \right.\,\left( {k \in \mathbb{Z}} \right)\)

\( \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{{40}} + k\pi \\x = - \frac{{9\pi }}{{40}} + k\pi \end{array} \right.\,\left( {k \in \mathbb{Z}} \right)\).