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Question
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
Solution
tan–1x + tan–1y + tan–1z = π
`tan^-1 [(x + y)/(1 - xy)] + tan^-1z = pi`
`tan^-1 [((x + y)/(1 - xy) + z)/(1 - ((x + y)/(1 - xy))z)] = pi`
`tan^-1 [((x + y + z(1 - xy))/(1 - xy))/((1 - xy - (xz + yz))/(1 - xy))] = pi`
`(x + y + z - zyz)/(1 - xy - xz - yz) = tanpi` = 0
x + y + z – xyz = 0
x + y + z = xyz
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