Intergration using trig substitution

I need to integrate 1/ (1 - x^2)^(1/2) dx

I know I can use x = sin theta but... I was also taught that I can use x = cos theta

When I do this I end up with the integral of - sin theta/ sin theta therefore

the antiderv is negative theta when I know it should be theta!!!! I know I then need to put the answer back in terms of x and add C. Using the sin sub I get arcsin of x + When I use cos sub I get - arccos of x + C!!!!!Could someone please tell me where I am making my mistake? Thanks again for all the time you folks devote! Frostking