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Let f(x)=sin((pi)/(6)sin((pi)/(2)sinx)) ...

Let `f(x)=sin((pi)/(6)sin((pi)/(2)sinx)) " for all "x in R and g(x)=(pi)/(2)sinx" for all " x in R`. Let `(fog)(x)` denote `f(g(x)) and (gof)(x)` denote `g(f(x)).` Then which of the following is (are) true?

A

Range of f is `[-1/2,1/2]`

B

Range of fog is `[-1/2,1/2]`

C

`underset(x to 0)lim (f(x))/(g(x))=pi/6`

D

There is `x in R" such that "(gof)(x)=1`

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