I keep having trouble with my trigonometric substitutions.

take for example:

integral from 0 to 1: dx / sqrt(1-x^2) (this also an improper integral)

Here's what I'm doing:

x=sin(t) dx=cos(t)

1-x^2 = cos(t)^2 <--trig identity of 1-sin^2 = cos^2

so now I have:

cos(t)/sqrt(cos(t)^2) which gives me:

cos(t)/ abs(cos(t)) = 1

however, i'm making a mistake. where?