Actually the given function is not defined when cos^-1(cos(x)) > sin^-1(sin(x)).

Here is a comparison of these two functions through graph.

Clearly see that from [0,pi/2] these functions are equal and from (pi/2,2pi) cos^-1(cos(x)) > sin^-1(sin(x)) and so our functions in not defined. Here i am only able to show the graph from (-pi,pi). 

Similarly on negative x-direction our function is not defined in (-3pi/2,0) and so on.

So, our function is defined in the interval ..........(-4pi,-7pi/2)U(-2pi,-3pi/2)U(0,pi/2)U(2pi,5pi/2)U(4pi,9pi/2)............

and it is the domain of given function.

thanx a ton bro

dis question was gettin on my nerves

thnx again!!!!!!