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Inverse Function

The principal...

Question

The principal value of ${sin}^{- 1} (- \frac{\sqrt{3}}{2})$ is

A

\frac{π}{3}

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B

- \frac{π}{3}

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C

\frac{π}{6}

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D

- \frac{π}{6}

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Solution

The correct option is B $- \frac{π}{3}$
Let the principal value be $y$
$y = {sin}^{- 1} (- \frac{\sqrt{3}}{2}), y \in [- \frac{π}{2}, \frac{π}{2}] \Rightarrow sin y = - \frac{\sqrt{3}}{2} \Rightarrow sin y = sin (- \frac{π}{3}) \Rightarrow y = - \frac{π}{3}$

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Inverse Function

Standard XII Mathematics

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