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:

D

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