The domain of the functionf(x) = Cos-1(sec (cos-1X)) + sin-1 (Cosec(sin-1  X)) is

f(x)=cos-1(sec(cos-1x)+sin-1(coses(sin-1x)) ⇒         -1≤sec(cos-1x)≤1 and      -1≤cosec (sin-1x)≤1 ⇒                  sec(cos-1x)=±1 and               cosec (sin-1x)=±1 ⇒cos-1x=0,π   and sin-1x=π2,-π2 ⇒                        x=±1 and x=±1 ∴  Domain is x=±1