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

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

A

`-2"cot"(x)/(2)-x+C`

B

`-2"cot"(x)/(2)+x+C`

C

`2"cot"(x)/(2)+x+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I-(2cos^(2)((x)/(2)))/(2sin^(2)((x)/(2)))dx=int"cot"^(2)(x)/(2)dx=int("cosec"^(2)(x)/(2)-1)dx`.
`="cosec"^(2)(x)/(2)-intdx=2"cosec"^(2)tdt-x+C`.
`=-2cott-x+C=-"cot"(x)/(2)-x+C`.
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