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STD 11 - 3. trignometrical ratios,functions and identities — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 3. trignometrical ratios,functions and identities4 Marks
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
    $21/221$
  • ✓
    $171/221$
✓

Answer

Correct option: D.
$171/221$
d
(d) Given, $\sin \alpha = \frac{{15}}{{17}},\tan \beta = \frac{{12}}{5}$

$ \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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