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Let f (x)= sin ^(-1) x-cos ^(-1) x, then...

Let `f (x)= sin ^(-1) x-cos ^(-1)` x, then the set of values of k for which of `|f (x)|=k` has exactly two distinct solutions is :

A

`(0,(pi)/(2)]`

B

`(0,(pi)/(2)]`

C

`[(pi)/(2), (3pi)/(2))`

D

`[pi, (3pi)/(2)]`

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The correct Answer is:
A
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