If `(x -1) (x^(2) + 1) gt 0`, then find the value of `sin((1)/(2) tan^(-1).(2x)/(1 - x^(2)) - tan^(-1) x)`

If `(x -1) (x^(2) + 1) gt 0`, then find the value of `sin((1)/(2) tan^

1.	If `(x -1) (x^(2) + 1) gt 0`, then find the value of `sin((1)/(2) tan^(-1).(2x)/(1 - x^(2)) - tan^(-1) x)`
Answer» `(x -1) (x^(2) + 1) gt 0` `:. Sin[(1)/(2) tan^(-1) ((2x)/(1 - x^(2))) - tan^(-1) x]` `= sin [(1)/(2) (-pi + 2 tan^(-1) x) - tan^(-1) x] = sin (-(pi)/(2)) = -1`

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