If $x \in (\frac{3 π}{2}, 2 π)$ , then the value of the expression ${sin}^{- 1} [cos {{cos}^{- 1} (cos x) + {sin}^{- 1} (sin x)}]$

- \frac{π}{2}

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\frac{π}{2}

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0

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π

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Solution

The correct option is B $\frac{π}{2}$
${sin}^{- 1} [cos {{cos}^{- 1} (cos x) + {sin}^{- 1} (sin x)}] ⟹ {sin}^{- 1} [cos {2 π - x + x - 2 π}] = {sin}^{- 1} [1] = \frac{π}{2}$

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