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* Hướng dẫn giải

\(\begin{array}{l}
{0^ \circ } < \alpha  < \beta  < {90^ \circ } \Rightarrow \left\{ \begin{array}{l}
0 < \sin \alpha  < \sin \beta \\
0 < c{\rm{os}}\beta  < c{\rm{os}}\alpha 
\end{array} \right.\\
 \Rightarrow \frac{{\sin \alpha }}{{c{\rm{os}}\alpha }} < \frac{{\sin \beta }}{{c{\rm{os}}\beta }},\frac{{c{\rm{os}}\alpha }}{{\sin \alpha }} > \frac{{c{\rm{os}}\beta }}{{\sin \beta }}\\
 \Rightarrow \tan \alpha  < \tan \beta ,\cot \alpha  > \cot \beta 
\end{array}\)