Domain of f(x) = cos-1x + cot-1x+ cosec-1x is

A [-1,1] B R C (-INFINITY,-1]U[1,INFINITY) D {-1,1}

ANswer is D. EXPLAIN PLEASE!

Domain of cos^-1x = [-1 ,1] 
Domain of cot^-1x = R
Domain of cosec^-1x = R - (-1,1)

So taking intersection of domains of all three we have  only {-1 ,1}
As cos^-1x is confined between [-1,1] and cosec^-1x is not defined between (-1,1) , so only -1 and 1 are left.
So option D is correct .