Giải phương trình: cot(2x + pi) = -1

Do \(\cot \left( { - \frac{\pi }{4}} \right) = - 1\) nên cot(3x + π) = – 1 \( \Leftrightarrow \cot \left( {3x + \pi } \right) = \cot \left( { - \frac{\pi }{4}} \right)\)

\( \Leftrightarrow 3x + \pi = - \frac{\pi }{4} + k\pi \,\,\,\left( {k \in \mathbb{Z}} \right)\)

\( \Leftrightarrow 3x = - \frac{{5\pi }}{4} + k\pi \,\,\,\left( {k \in \mathbb{Z}} \right)\)

\( \Leftrightarrow x = - \frac{{5\pi }}{{12}} + k\frac{\pi }{3}\,\,\,\left( {k \in \mathbb{Z}} \right)\).