Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Integrals
0 votes

Find the integrals of the functions\[\frac{1-\cos x}{1+\cos x}\]

$\begin{array}{1 1} 2\tan \frac{x}{2}-x+c. \\ 2\tan \frac{x}{2}+x+c \\ 2\cot \frac{x}{2}-x+c \\ 2\cot \frac{x}{2}+x+c. \end{array} $

Can you answer this question?

1 Answer

0 votes
  • (i)$1-\cos x=2\sin^2\frac{x}{2}$.
  • (ii)$1+\cos x=2\cos^2\frac{x}{2}$.
  • (iii)$\int \tan xdx=log|\sec x|+c.$
  • (iv)$\sec^2xdx=\tan x+c.$
Given $I=\int\frac{1-\cos x}{1+\cos x}dx.$
Using the information in the tool box we get
$1-\cos x=2\sin^2\frac{x}{2}$ and $1+\cos x=2\cos^2\frac{x}{2}$.
But $\tan^2\frac{x}{2}=\sec^2\frac{x}{2}-1$.
Substituting this,
On separating the terms,
$\;\;\;=\int\sec^2\frac{x}{2}dx-\int dx.$
On integrating we get,


answered Jan 30, 2013 by sreemathi.v
Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App