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int(1-cosx)cosec^(2)x dx is equal to...

`int(1-cosx)cosec^(2)x dx` is equal to

A

`tan x+C`

B

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

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`int(1-cosx)"cosec"^(2)xdx`
`=int"cosec"^(2)xdx-int"cosec"^(2)xcosxdx`
`=-cotx+"cosec x"+C=(1-cosx)/(sinx)+C`
`=(2sin^(2).(x)/(2))/(2sin.(x)/(2)cos.(x)/(2))+C`
`=tan.(x)/(2)+C`
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