Integrate the functions`(1-cosx)/(1+cosx)`

1.	Integrate the functions`(1-cosx)/(1+cosx)`
Answer» We know, `cosx = 2cos^2(x/2) - 1 => 1+cosx = 2cos^2(x/2)` Also, `cosx = 1 - 2sin^2(x/2) => 1-cosx = 2sin^2(x/2)` `:. (1-cosx)/(1+cosx) = (2sin^2(x/2))/(2sin^2(x/2)) = tan^2(x/2).` `:. int (1-cosx)/(1+cosx) dx = int tan^2(x/2)dx` `= int (sec^2(x/2) - 1) dx` `= tan (x/2)/(1/2) - x +c` `:. int (1-cosx)/(1+cosx) dx = 2 tan (x/2) - x+c.`

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