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$f (x) = {Tan}^{- 1} (\sin x)$ is decreasing in

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$(2 n π - \frac{π}{2}, 2 n π + \frac{π}{2})$

$(2 n π + \frac{π}{2}, 2 n π + \frac{3 π}{2})$

$(\frac{π}{2}, \frac{3 π}{2})$

$(\frac{- π}{2}, \frac{π}{2})$

answer is B.

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Detailed Solution

$f^{1} (x) = \frac{\cos x}{1 + \sin^{2} x}, f (x) is decreasing$

$f^{'} (x) < 0 \cos x < 0 x \in (\frac{π}{2}, \frac{3 π}{2})$

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