The integral of
$$ \int \frac{1}{\sqrt{1-x^{2}}} dx $$
with substitution $x=\sin(\theta)$ is
$$ \int \frac{\cos(\theta)}{\sqrt{\cos^{2}(\theta)}} d \theta$$
If I notice, this can take two form, since it can be written as
$$ \int \frac{\cos(\theta)}{|\cos(\theta)|} d \theta$$
But why some textbooks (from what I have seen, for example : *Schaum's outline of Calculus*) does not account this? which means only take the positive value
$$ \int \frac{\cos(\theta)}{\sqrt{\cos^{2}(\theta)}} d \theta = \int d \theta$$
Or, am i missing something here?

I presume that it is for simplicity in explanation. If so, which is the better one to be explained to freshmen students?
Thanks.