Cho \(\cot \alpha  = \frac{1}{2}\left( {\pi  var DOMAIN = "...

* Hướng dẫn giải

\(\begin{array}{l}
\sin \alpha  =  - \sqrt {\frac{1}{{1 + {{\cot }^2}\alpha }}}  =  - \frac{{2\sqrt 5 }}{5}\\
 \Rightarrow \cos \alpha  =  - \sqrt {1 - {{\sin }^2}\alpha }  =  - \frac{{\sqrt 5 }}{5}\left( {\pi  < \alpha  < \frac{3}{2}} \right)\\
 \Rightarrow {\sin ^2}\alpha .\cos \alpha  = \frac{{ - 4}}{{5\sqrt 5 }}
\end{array}\)