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int(1-cosx)/(cosx(1+cosx))dx...

`int(1-cosx)/(cosx(1+cosx))dx`

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`frac{1-cos x}{cos x(1+cos x)}=frac{1-t}{t(1+t)} `

`=(frac{1}{t}-frac{2}{1+t})=(frac{1}{cos x}-frac{2}{1+cos x})`

Therefore,

`I=int(frac{1}{cos x}-frac{2}{1+cos x}) d x=int(sec x-sec ^{2} frac{x}{2}) d x `

`=log (sec x+tan x)-2 tan (frac{x}{2})`

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