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}$

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

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