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

The value of
`tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))],|x|lt1/2` x is `!=0` equal to

A

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

B

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

C

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

D

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

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The correct Answer is:
A
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