Find domain for `f(x)=sqrt(cos (sin x))`

Explanation

`f(x) = sqrt(cos(sinx))` is defined if
`cos(sinx) ge 0`

As we know, `-1 le sin x le 1` for all x.
So, `cos theta ge 0`
` " " ` (Here, `theta=sin x` lies in the first and fourth quadrants)
i.e., ` cos(sin x) ge 0` for all x
i.e., ` x in R`
Thus, the dimain f(x) is R.