If f(x)=sin^(-1)x and g(x)=[sin(cosx)]+[...

If f(x)=`sin^(-1)x` and g(x)=[sin(cosx)]+[cos(sinx)], then range of f(g(x)) is (where `[*]` denotes greatest integer function)

A

`{(-pi)/2,pi/2}`

B

`{(-pi)/2,0}`

C

`{0,pi/2}`

D

`{-pi/2,0,pi/2}`

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The correct Answer is:

C

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