Đáp án:
$A = - \cot \left( {\dfrac{x}{4}} \right)$
Giải thích các bước giải:
$\begin{array}{l}
A = \dfrac{{1 + \cos \left( {\dfrac{x}{2}} \right) - \sin \left( {\dfrac{x}{2}} \right)}}{{1 - \cos \left( {\dfrac{x}{2}} \right) - \sin \left( {\dfrac{x}{2}} \right)}}\\
= \dfrac{{2{{\cos }^2}\left( {\dfrac{x}{4}} \right) - 2\sin \left( {\dfrac{x}{4}} \right)\cos \left( {\dfrac{x}{4}} \right)}}{{2{{\sin }^2}\left( {\dfrac{x}{4}} \right) - 2\sin \left( {\dfrac{x}{4}} \right)\cos \left( {\dfrac{x}{4}} \right)}}\\
= \dfrac{{2\cos \left( {\dfrac{x}{4}} \right)\left( {\cos \left( {\dfrac{x}{4}} \right) - \sin \left( {\dfrac{x}{4}} \right)} \right)}}{{2\sin \left( {\dfrac{x}{4}} \right)\left( {\sin \left( {\dfrac{x}{4}} \right) - \cos \left( {\dfrac{x}{4}} \right)} \right)}}\\
= - \dfrac{{\cos \left( {\dfrac{x}{4}} \right)}}{{\sin \left( {\dfrac{x}{4}} \right)}}\\
= - \cot \left( {\dfrac{x}{4}} \right)
\end{array}$
