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If x(1) = 2 tan^(-1) ((1 + x)/(1 -x)), x...

If `x_(1) = 2 tan^(-1) ((1 + x)/(1 -x)), x_(2) = sin^(-1) ((1 - x^(2))/(1 + x^(2))), " where " x in (0, 1)`, then 2(`x_(1) + x_(2)`) is equal to

A

0

B

`2pi`

C

`pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`x_(1) = 2 tan^(-1) ((1 + x)/(1 - x))`
and `x_(2) = sin^(-1) ((1 - x^(2))/(1 + x^(2)))`
`= tan^(-1) ((1 - x^(2))/(2x))`
Now `(1 + x)/(1 -x) gt 1`
`rArr x_(1) = pi + tan^(-1) ((2((1 + x)/(1 -x)))/(1 -((1+ x)/(1 -x))^(2)))`
`= pi + tan^(-1) ((1 -x^(2))/(-2x))`
`= pi - tan^(-1) ((1 -x^(2))/(2x))`
`rArr x_(1) + x_(2) = pi`
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