Evaluate the following integrals:

Question:

Evaluate the following integrals:

$\int \sqrt{\frac{1-\cos x}{1+\cos x}} d x$

Solution:

$1-\cos x=2 \sin ^{2} \frac{x}{2}$

$1+\cos x=2 \cos ^{2} \frac{x}{2}$

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

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

$\Rightarrow \int \tan \frac{x}{2} d x$

$\Rightarrow-2 \ln \left|\cos \frac{x}{2}\right|+c$

Leave a comment

None
Free Study Material