The domain of f(x)=cos(sinx)  is

f(x)=cos⁡(sin⁡x) is defined if cos⁡(sin⁡x)≥0----(1) As we know, −1≤sin⁡x≤1 for all x∈R . So, cos⁡θ≥0 (Here, θ=sin⁡x lies in the first and fourth quadrants)  i.e., cos⁡(sin⁡x)≥0 for all x i.e., x∈R Thus, the domain of f(x) is R .