Let f(x)=lim( n to oo)(cosx)/(1+(tan^(-1...

Let `f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n))`. Then the value of `int_(o)^(oo)f(x)dx` is equal to

A

`cos (tan 1)`

B

`sin(tan1)`

C

`tan(tan1)`

D

none of these

Verified by Experts

The correct Answer is:

B

`I=int_(0)^(tan1)f(x)dx+int_(tan1)^(oo)f(x)dx`
`=int_(0)^(tan1)cosxdx+0`
`=sin(tan1)`

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