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

∫[(1-cosx)/(1+cosx)]dx

=∫[2sin²(x/2)/2cos²(x/2)]dx

=∫tan²(x/2)dx

and integrate further.

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)