If `x + y + z = xyz and x, y, z gt 0`, then find the value of `tan^(-1) x + tan^(-1) y + tan^(-1) z`

If `x + y + z = xyz and x, y, z gt 0`, then find the value of `tan^(-1

1.	If `x + y + z = xyz and x, y, z gt 0`, then find the value of `tan^(-1) x + tan^(-1) y + tan^(-1) z`
Answer» Correct Answer - `pi` `xy = 1 _ (x)/(z) + (y)/(z) gt 1` `rArr tan^(-1) x + tan^(-1) y + tan^(-1) z` `= pi + tan^(-1) [(x + y)/(1 - xy)] + tan^-(1) z` `= pi + tan^(-1) [(xyz -z)/(1 - xy)] + tan^(-1) z` `= pi + tan^(-1) [(z (xy -1))/(1 -xy)] + tan^(-1) z` `= pi + tan^(-1) (-z) + tan^(-1) z = 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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