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Evaluate int(1-cosx)"cosec"^(2)xdx...

Evaluate `int(1-cosx)"cosec"^(2)xdx`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
(a) `int(1-cos x)"cosec"^(2)x dx=int(1-cosx)/(1-cos^(2)x)dx`
`=int(1)/(1+cosx)dx=(1)/(2)int sec^(2).(x)/(2)dx=tan.(x)/(2)+C`
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