The domain of the function f(x)=sin-1(sin x)-cos-1(cos x) in 0,2π is

As, sin-1(sin x) could be sketched, asand cos-1(cos x) could be sketched as ∴sin-1(sin x)>cos-1(cos x) is not possible.Only equality holds as Thus, sin-1sin x=cos-1cos xWhen                  x∈0,π2∪3π2,2πSo, domain for f(x) is 0,π2∪3π2,2πHence, (a) is the correct answer.