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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

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π2

−π2

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Correct option is B

x∈π2,π⇒sinsin-1x=π-x∴sin-1coscoscos-1x+sinsin-1x=sin-1cosx+π-x =sin-1-1 =-π2

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The value of sin−1coscos−1cosx+sin−1sinxwhere x∈π2,πis

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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