Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
0 < \alpha < \frac{\pi }{2} \Rightarrow \left\{ \begin{array}{l}
\sin \alpha > 0\\
\cos \alpha > 0
\end{array} \right.\\
{\sin ^2}\alpha + {\cos ^2}\alpha = 1\\
\Leftrightarrow {\sin ^2}\alpha + {\left( {\frac{4}{{13}}} \right)^2} = 1\\
\Leftrightarrow {\sin ^2}\alpha = \frac{{153}}{{169}} \Rightarrow \sin \alpha = \frac{{3\sqrt {17} }}{{13}}\,\,\,\,\,\,\,\,\left( {\sin \alpha > 0} \right)\\
\Rightarrow \tan \alpha = \frac{{\sin \alpha }}{{\cos \alpha }} = \frac{{3\sqrt {17} }}{4}\\
\cot \alpha = \frac{{\cos \alpha }}{{\sin \alpha }} = \frac{4}{{3\sqrt {17} }}
\end{array}\)
