Đáp án:
\(\begin{array}{l}
\tan \alpha = \frac{1}{{\sqrt 3 }}\\
\cot \alpha = \sqrt 3
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
{\cos ^2}\alpha + {\sin ^2}\alpha = 1\\
\to \frac{3}{4} + {\sin ^2}\alpha = 1\\
\to {\sin ^2}\alpha = \frac{1}{4}\\
Do:\alpha \in \left( {\frac{\pi }{2};\pi } \right)\\
\to \sin \alpha > 0\\
\to \sin \alpha = \frac{1}{2}\\
\to \tan \alpha = \frac{{\sin \alpha }}{{\cos \alpha }} = \frac{1}{2}.\frac{2}{{\sqrt 3 }} = \frac{1}{{\sqrt 3 }}\\
\to \cot \alpha = \frac{1}{{\tan \alpha }} = \sqrt 3
\end{array}\)
