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The Integral int(pi/4)^((3pi)/4)(dx)/(1+...

The Integral `int_(pi/4)^((3pi)/4)(dx)/(1+cosx)` is equal to: (2) (3) (4)

A

`-2`

B

2

C

4

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `I=int_(pi//4)^(3pi//4)(dx)/(1+cosx)=int_(pi//4)^(3pi//4)(1-cosx)/(1-cos^(2)x)dx`
`= int_(pi//4)^(3pi//4)(1-cosx)/(sin^(2)x)dx`
`=int_(pi//4)^(3pi//4)("cosec"^(2)x-"cosec" x cot x)dx`
`=[-cotx+"cosec"x]_(pi//4)^(3pi//4)`
`[(1+sqrt(2))-(-1+sqrt(2))]=2`
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