If \( f(x)=\max .\left\{\sin x, \sin ^{-1}(\cos x)\right\} \), then...

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If \( f(x)=\max .\left\{\sin x, \sin ^{-1}(\cos x)\right\} \), then :
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(a) \( f \) is differentiable every where
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(b) \( f \) is continuous every where but not differentiable
(c) \( f \) is discontinuous at \( x=\frac{n \pi}{2}, n \in I \)
(d) \( f \) is non-differentiable at \( x=\frac{n \pi}{2}, n \in I \)
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