Đáp án:
$S = \{ \frac{1}{3} + \frac{{2k}}{3},k \in Z\} $
Giải thích các bước giải:
$\begin{array}{l}
\tan \left( {x.\frac{\pi }{2}} \right) = \cot (x.\pi )\\
< = > \tan \left( {x.\frac{\pi }{2}} \right) = \tan \left( {\frac{\pi }{2} - x\pi } \right)\\
< = > x.\frac{\pi }{2} = \frac{\pi }{2} - x\pi + k\pi \\
< = > x\left( {\frac{\pi }{2} + \pi } \right) = \frac{\pi }{2} + k\pi \\
< = > x.\frac{{3\pi }}{2} = \frac{\pi }{2} + k\pi \\
< = > x.\frac{3}{2} = \frac{1}{2} + k\\
< = > x = \frac{1}{3} + \frac{{2k}}{3},k \in Z\\
= > S = \{ \frac{1}{3} + \frac{{2k}}{3},k \in Z\}
\end{array}$
