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

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

Text Solution

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`int(1-cosx)/(1+cosx)dx=int((1-cosx)^(2))/(1-cos^(2)x)dx`
`=int(1-2cosx+cos^(2)x)/(sin^(2)x)dx`
`=int("cosec"^(2)x-2"cosec"xcotx+cot^(2)x)dx`
`=int(2"cosec"^(2)x-2"cosec"xcotx-1)dx`
`=-2cotx +2 "cosec"x-x+c`
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