Đáp án:
$\begin{array}{l}
A = \sin \left( {3\pi + x} \right) - \cos \left( {\frac{{9\pi }}{2} - x} \right)\\
+ \cot \left( {2\pi - x} \right) + \tan \left( {\frac{\pi }{2} - x} \right)\\
= - \sin x - \sin x - \cot x + \cot x\\
= - 2\sin x
\end{array}$
$\begin{array}{l}
b)\tan x = 2 = \dfrac{{\sin x}}{{\cos x}}\\
\Leftrightarrow \sin x = 2\cos x\\
A = \dfrac{{2{{\sin }^2}x - 5\sin x.\cos x + {{\cos }^2}x}}{{2{{\sin }^2}x + \sin x.\cos x + {{\cos }^2}x}}\\
= \dfrac{{2.4{{\cos }^2}x - 5.2\cos x.\cos x + {{\cos }^2}x}}{{2.4{{\cos }^2}x + 2.\cos x.\cos x + {{\cos }^2}x}}\\
= \dfrac{{8 - 10 + 1}}{{8 + 2 + 1}}\\
= \dfrac{{ - 1}}{{11}}
\end{array}$
