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If (x-1)(x^2+1)>0 , then find the value ...

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