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If (x -1) (x^(2) + 1) gt 0, then find th...

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)`

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`(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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