Đáp án:
$\begin{array}{l}
A = \tan \alpha \left( {\dfrac{{1 + {{\cos }^2}\alpha }}{{\sin \alpha }} - \sin \alpha } \right) = \tan \alpha \left( {\dfrac{{1 + {{\cos }^2}\alpha - {{\sin }^2}\alpha }}{{\sin \alpha }}} \right) = \tan \alpha \left( {\dfrac{{\left( {1 - {{\sin }^2}\alpha } \right) + {{\cos }^2}\alpha }}{{\sin \alpha }}} \right)\\
= \tan \alpha .\dfrac{{2{{\cos }^2}\alpha }}{{\sin \alpha }} = 2\tan \alpha .\cot \alpha .\cos \alpha = 2\cos \alpha
\end{array}$
