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int(dx)/((1-cosx))=?...

`int(dx)/((1-cosx))=?`

A

`(1)/((x-sinx))+C`

B

`log|x-sinx|+C`

C

`log|"tan"(x)/(2)|+C`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
`I=int(dx)/(2sin^(2)((x)/(2)))=(1)/(2)int"cosec"^(2)((x)/(2))dx`.
`int"cosec"^(2)"t dt, where"(x)/(2)=t anddx=2dt`
`=-cot t+C=-cot((x)/(2))+C`.
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