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Inverse Trigonometric Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSInverse Trigonometric Functions1 Mark
Question
Find the value of ${\sin ^{ - 1}}\left( {\sin \frac{{3\pi }}{5}} \right)$ 
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Answer

${\sin ^{ - 1}}\left( {\sin \frac{{3\pi }}{5}} \right) = ?$
${\sin ^{ - 1}}\left( {\sin \frac{{3\pi }}{5}} \right) = {\sin ^{ - 1}}\left[ {\sin \left( {\pi - \frac{{3\pi }}{5}} \right)} \right]$
$=\sin^{​​​​-1}(\sin \frac{2\pi}{5}$)
$[\because {\sin ^{ - 1}}(\sin \theta )] = \theta $
When $\theta \in \left[ {\frac{{ - \pi }}{2},\frac{\pi }{2}} \right]$
$=​ {\frac{{2\pi }}{5}}$

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