Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow - \pi < \alpha - \frac{{3\pi }}{2} < - \frac{\pi }{2} \Rightarrow \sin \left( {\alpha - \frac{{3\pi }}{2}} \right) < 0\\
b,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow - \frac{\pi }{2} < \frac{\pi }{2} - \alpha < 0 \Rightarrow \left\{ \begin{array}{l}
\sin \left( {\frac{\pi }{2} - \alpha } \right) < 0\\
\cos \left( {\frac{\pi }{2} - \alpha } \right) > 0
\end{array} \right. \Rightarrow \cot \left( {\frac{\pi }{2} - \alpha } \right) < 0\\
c,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow - \pi < \alpha - \frac{{3\pi }}{2} < - \frac{\pi }{2} \Rightarrow \cos \left( {\alpha - \frac{{3\pi }}{2}} \right) < 0\\
d,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow \pi < \frac{\pi }{2} + \alpha < \frac{{3\pi }}{2} \Rightarrow \left\{ \begin{array}{l}
\sin \left( {\frac{\pi }{2} + \alpha } \right) < 0\\
\cos \left( {\frac{\pi }{2} + \alpha } \right) < 0
\end{array} \right. \Rightarrow \tan \left( {\frac{\pi }{2} + \alpha } \right) > 0\\
e,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow \frac{{3\pi }}{2} < \frac{{5\pi }}{2} - \alpha < 2\pi \Rightarrow \left\{ \begin{array}{l}
\sin \left( {\frac{{5\pi }}{2} - \alpha } \right) < 0\\
\cos \left( {\frac{{5\pi }}{2} - \alpha } \right) > 0
\end{array} \right. \Rightarrow \cot \left( {\frac{{5\pi }}{2} - \alpha } \right) < 0\\
f,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow 2\pi < \alpha + \frac{{3\pi }}{2} < \frac{{5\pi }}{2} \Rightarrow \sin \left( {\alpha + \frac{{3\pi }}{2}} \right) > 0
\end{array}\)
