Find the range of `f(x)=sin(cosx).`

Explanation

`f(x)=sqrt(cos(sinx))+sqrt(sin(cosx))`
Period of `f(x)` is `2 pi`.
Also, `sin(cosx) ge 0 impliescosx in [0,1]`
`implies x in [-(pi)/(2),(pi)/(2)]`
` :. x` lies in `1^(st)` and `4^(th)` quadrants.
Also `f(-x)=f(x)`
` :. f(x)` is even.
` :. ` we need to find the range in `[0,(pi)/(2)]` only
In `[0,(pi)/(2)], sinx` increases, but `cosx` decreases
` :. " both " cos(sinx) and sin(cosx)` decrease.
Hence `f(x)` decreases,
` :. ` Range is `[f(pi//2),f(0)] -=[sqrt(cos 1),1+sqrt(sin1)]`