The function f(x)=sin−1(cosx) is

Since both cosx  and sin−1x are continuous function, f(x)=sin−1(cosx)  is also a continuous function. Now,f1(x)=sin−1x1−cos2x=sinx|sinx|={−sinx−sinx=1,x<0−sinxsinx=−1,x>0 ∴(L.H.D.atx=0)=1  and∴(R.H.D.atx=0)=−1 Hence f(x)  is not differentiable atx=0.