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

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

A

`(1)/(2)"tan"(x)/(2)+C`

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int(dx)/(2cos^(2)((x)/(2)))=(1)/(2)intsec^(2)((x)/(2))dx`.
`=intsec^(2)tdt," where "(x)/(2)=t anddx=2dt`
`=tant+C="tan"(x)/(2)+C`.
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