The value of sin−1⁡cos⁡sin−1⁡−32 is - Infinity Learn by Sri Chaitanya

A
$\frac{π}{3}$
B
$\frac{π}{6}$
C
$\frac{- π}{3}$
D
$\frac{- π}{6}$

Solution:

$\sin^{- 1} [\cos \{\sin^{- 1} (- \frac{\sqrt{3}}{2})\}]$

$\begin{matrix} = \sin^{- 1} \{\cos (- \frac{π}{3})\} [∵ \sin^{- 1} (- \frac{\sqrt{3}}{2}) = - \frac{π}{3}] \\ = \sin^{- 1} (\cos \frac{π}{3}) = \sin^{- 1} (\frac{1}{2}) = \frac{π}{6} \end{matrix}$

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