Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\tan \alpha = \frac{1}{{\cot \alpha }} = \sqrt 3 \\
\cot \alpha = \frac{{\sqrt 3 }}{3} \Leftrightarrow \frac{{\cos \alpha }}{{\sin \alpha }} = \frac{{\sqrt 3 }}{3} \Leftrightarrow 3\cos \alpha = \sqrt 3 \sin \alpha \Leftrightarrow \sin \alpha = \sqrt 3 \cos \alpha \\
{\sin ^2}\alpha + {\cos ^2}\alpha = 1\\
\Leftrightarrow {\left( {\sqrt 3 \cos \alpha } \right)^2} + {\cos ^2}\alpha = 1\\
\Leftrightarrow {\cos ^2}\alpha = \frac{1}{4}\\
\Leftrightarrow \left[ \begin{array}{l}
\cos \alpha = \frac{1}{2} \Rightarrow \sin \alpha = \frac{{\sqrt 3 }}{2}\\
\cos \alpha = - \frac{1}{2} \Rightarrow \sin \alpha = - \frac{{\sqrt 3 }}{2}
\end{array} \right.
\end{array}\)
