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Q8  Find the integrals of the functions \frac{1- \cos x }{1+ \cos x }

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best_answer

We know the identities

\\1+\cos 2A = 2\cos^2A\\ 1-\cos 2A = 2\sin^2 A

Using the above relations we can write

\frac{1-\cos x}{1+\cos x}=\frac{\sin^2x/2}{\cos^2x/2} = \tan^2x/2

                                               =\int \tan^2x/2 =\int (\sec^2x/2-1)dx
                                                                              \\=\int (\sec^2x/2)dx-\int dx\\ = 2[\tan x/2]-{x}+C

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manish

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