Question:
Evaluate the following integrals:
$\int \sqrt{\frac{1-\cos x}{1+\cos x}} d x$
Solution:
$1-\cos x=2 \sin ^{2} \frac{x}{2}$
$1+\cos x=2 \cos ^{2} \frac{x}{2}$
$\Rightarrow \int \sqrt{\frac{2 \sin ^{2} \frac{x}{2}}{2 \cos ^{2} \frac{x}{2}}} d x$
$\Rightarrow \int \sqrt{\tan ^{2} \frac{x}{2}} d x$
$\Rightarrow \int \tan \frac{x}{2} d x$
$\Rightarrow-2 \ln \left|\cos \frac{x}{2}\right|+c$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.