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The value of $\sin^{- 1} [\cos {\cos^{- 1} (\cos x) + \sin^{- 1} (\sin x)}]$ where $x \in (\frac{π}{2}, π)$ is equal to

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Correct option is D

sin−1cos{cos−1(cosx)+sin−1(sinx)}=sin−1[cos(x+π−x)] ∵sin-1sinx=sin-1sinπ-x=π-x ∵x∈π2,π⇒π2

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The value of sin−1[cos{cos−1(cosx)+sin−1(sinx)}]where x∈(π2,π)is equal to

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The value of $\sin^{- 1} [\cos {\cos^{- 1} (\cos x) + \sin^{- 1} (\sin x)}]$ where $x \in (\frac{π}{2}, π)$ is equal to