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 `x_(1) + x_(2)` is equal to

If `x_(1) = 2 tan^(-1) ((1 + x)/(1 -x)), x_(2) = sin^(-1) ((1 - x^(2))

1.	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 `x_(1) + x_(2)` is equal to
Answer» Correct Answer - 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`

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
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