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Then integral int(pi//4)^((3pi)/4) (dx)/...

Then integral `int_(pi//4)^((3pi)/4) (dx)/(1+cosx)` is equal to

A

`1`

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I = int_(-pi//4)^(pi//4)(dx)/(1+cos2x) = int_(-pi//4)^(pi//4)(dx)/(2cos^(2)x)`
`= 1/2int_(-pi//4)^(pi//4) sec^(2)xdx = int_(0)^(pi//4) sec^(2)xdx = [tanx]_(0)^(pi//4) = 1`
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