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  4. The value of sin-1 [cos cos-1 (cos x) + sin-1 (sin x) ] where x∈((π/2), π) is equal to

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

Inverse Trigonometric Functions

Solution:

$sin^{-1} [cos \{cos^{-1} (cos\,x) + sin^{-1} (sin\,x)\}]$
$= sin^{-1} [cos(x + \pi - x)]$ as $x \in (\pi/2, \pi)$
$= sin^{-1} (cos\,\pi) = sin^{-1}(-1) = -\frac{\pi}{2}$