If `tan^(- 1)x+tan^(- 1)y+tan^(- 1)z=pi` prove that `x+y+z=xyz`

1.	If `tan^(- 1)x+tan^(- 1)y+tan^(- 1)z=pi` prove that `x+y+z=xyz`
Answer» `tan^(-1) x + tan ^(-1) y + tan ^(-1)z =pi ` `rArr " "tan^(-1).(x+y)/(1-xy) + tan^(-1) z = pi` `tan^(-1) .((x+y)/(1-xy))/(1-(x+y)/(1-xy)z)` `rArr (x+y +z(1-xy))/(1-xy -(x+y)z)= tan pi =0` `rArr " m " x+y + z -xyz =0` `rArr" "x +y + z =xyz`

Discussion

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