Evaluate the following integrals:
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)

$\Rightarrow \int \sqrt{\frac{2 \cos ^{2} x}{2 \sin ^{2} x}} d x$

$\Rightarrow \int \sqrt{\cot ^{2} x} d x$

$\Rightarrow \int \cot x d x$

$\Rightarrow \ln |\sin x|+c$

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