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The value of ...

Question

The value of ${sin}^{- 1} (sin \frac{5 π}{6})$ is

A

\frac{π}{6}

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B

\frac{5 π}{6}

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C

\frac{7 π}{6}

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D

- \frac{π}{6}

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Solution

The correct option is A $\frac{π}{6}$
${sin}^{- 1} (sin \frac{5 π}{6}) = {sin}^{- 1} (sin (π - \frac{π}{6})) = {sin}^{- 1} (sin (\frac{π}{6})) = \frac{π}{6} (∵ {sin}^{- 1} (sin x) = x, x \in [- \frac{π}{2}, \frac{π}{2}])$

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