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what are the steps involved to integrate 1-cosx/1+cosx to get the answer 2tan(x/2)-x+c ?

what are the steps involved to integrate 1-cosx/1+cosx to get the answer 2tan(x/2)-x+c ?

Grade:

2 Answers

Menka Malguri
39 Points
9 years ago

∫[(1-cosx)/(1+cosx)]dx

=∫[2sin²(x/2)/2cos²(x/2)]dx

=∫tan²(x/2)dx

and integrate further.

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Nanda,

 

The approach is exactly as posted by Menka.

 

Once you get tan^(x/2), write that as sec^2(x/2) - 1

 

Now Integral sec^2(x/2) is directly tan(x/2)*2

and integral of 1 is x.

 

So required result, 2tan(x/2) - x + constant.

 

Regards,

Ashwin (IIT Madras)

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