Giải phương trình:

\(\cot \left( {x + \frac{\pi }{5}} \right) = 1\).

Do \(\cot \frac{\pi }{4} = 1\) nên \(\cot \left( {x + \frac{\pi }{5}} \right) = 1\)\( \Leftrightarrow \cot \left( {x + \frac{\pi }{5}} \right) = \cot \frac{\pi }{4}\)

\( \Leftrightarrow x + \frac{\pi }{5} = \frac{\pi }{4} + k\pi \,\,\,\left( {k \in \mathbb{Z}} \right)\)

\( \Leftrightarrow x = \frac{\pi }{{20}} + k\pi \,\,\,\left( {k \in \mathbb{Z}} \right)\).