The value of tan^(-1)[(sqrt(1+x^2)+sqrt(...

The value of `tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))], |x|<1/2,x!=0`, is equal to:

A

`(pi)/(4)+(1)/(2)cos^(-1)x^(2)`

B

`(pi)/(4)+cos^(-1)x^(2)`

C

`(pi)/(4)+(1)/(2)cos^(-1)x`

D

`(pi)/(4)-(1)/(2)cos^(-1)x`

Verified by Experts

The correct Answer is:

A

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