Are the functions $\arcsin x$ and $\arccos x$ equal up to a constant?
When I was solving the indefinite integral $\int\frac{\mathrm dx}{\sqrt{1-x^2}}$ I got two different results depending on the kind of the trigonometric substitution I make:
$\displaystyle \int\frac{\mathrm dx}{\sqrt{1-x^2}}=-\arcsin x$, if $x=\sin \theta$
$\displaystyle \int\frac{\mathrm dx}{\sqrt{1-x^2}}=\arccos x$, if $x=\cos\theta$
Where's my mistake?