Archive
21st of March 2017
Mathematics
Q:

As directed by you I had posed the following question on Ask the Expertintegral subscript 0 superscript pi divided by 2 end superscript fraction numerator x d x over denominator 1 plus e sin x end fraction

In the solution the expert has used the identityintegral fraction numerator d x over denominator a plus b space cos x end fraction space equals space fraction numerator 1 over denominator square root of a squared minus space b squared end root end fraction cos to the power of negative 1 end exponent x space left parenthesis fraction numerator b plus a cos x over denominator a plus b cos x end fraction right parenthesis

Please can you explain or prove this identity as the same is not clear to me. If you want me to pose this question on Ask the Expert then please see that this feature is working properly on site of topper learning as when I tried using this feature today, it was not working properly.

Ahuja8087 Ahuja - CBSE - Class XII Science

Tuesday, March 21, 2017 at 18:04:PM

A:

begin mathsize 16px style Here comma space we space can space use space the space method space straight t equals tan straight x over 2 space and space half space angle space formula space for space cos space straight x
and space solve space it
straight x equals 2 tan to the power of negative 1 end exponent straight t
dx equals fraction numerator 2 dt over denominator 1 plus straight t squared end fraction
cosx space equals space fraction numerator 1 minus tan squared begin display style bevelled straight x over 2 end style over denominator 1 plus tan squared bevelled straight x over 2 end fraction equals fraction numerator 1 minus straight t squared over denominator 1 plus straight t squared end fraction end style

Tuesday, March 21, 2017 at 18:12:PM