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Evaluate int (x-sinx)/(1-cosx)dx....

Evaluate `int (x-sinx)/(1-cosx)dx`.

A

` log|1+cosx|+C`

B

`log|x+sinx|+C`

C

`x-tan'(x)/(2)+C`

D

`x.tan'x/2 + C`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I = int(x+sinx)/(1+cosx)dx`
`= int(x)/(1+cosx) dx + int (2sinx//2cosx//2)/(2cos^(2)x//2)dx`
`= int(x)/(2cos^(2)x//2)dx+int(2sinx//2cosx//2)/(2cos^(2)x//2)dx`
`= 1/2 intx sec^(2)x//2dx +inttanx//2dx`
`= 1/2[x.tanx//2.2-f tan'(x)/(2).2dx]+tan'x/2 dx`
`= x.tan 'x/2 + C`
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