MCQ
If $\frac{\pi }{2} < \alpha < \pi ,\,{\rm{ }}\pi < \beta < \frac{{3\pi }}{2};$ $\sin \alpha = \frac{{15}}{{17}}$ and $\tan \beta = \frac{{12}}{5}$, then the value of $\sin (\beta - \alpha )$ is
- A$-171/221$
- B$-21/221$
- C$21/221$
- ✓$171/221$
$ \Rightarrow \cos \alpha = \frac{8}{{17}},\sin \beta = \frac{{12}}{{13}}$
and $\cos \beta = - \frac{5}{{13}}$
==> $\pi < \beta < \frac{{3\pi }}{2}$,
$\therefore \cos \beta = - \frac{5}{{13}}$
$\sin (\beta - \alpha ) = \sin \beta \cos \alpha - \cos \beta \sin \alpha $ = $\frac{{171}}{{221}}$.
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