Question:
Evaluate the following integrals:
$\int \sqrt{\frac{1+\cos 2 x}{1-\cos 2 x}} d x$
Solution:
$1+\cos 2 x=2 \cos ^{2} x$
$1-\cos 2 x=2 \sin ^{2} x$
(both of them are trigonometric formuales)
$\Rightarrow \int \sqrt{\frac{2 \cos ^{2} x}{2 \sin ^{2} x}} d x$
$\Rightarrow \int \sqrt{\cot ^{2} x} d x$
$\Rightarrow \int \cot x d x$
$\Rightarrow \ln |\sin x|+c$