If tan-1x+tan-1y+tan-1z=pie, prove x+y+z=xyz

TAN-1X + TAN-1Y + TAN-1Z = PIE

TAN-1 ( X + Y / 1- XY) + TAN-1Z = PIE { TAN-1X + TAN-1Y = TAN-1 ( X + Y / 1- XY) }

TAN-1 ( X + Y / 1-XY) + Z = PIE

1- Z[(X + Y) /(1-XY)]

(X + Y / 1 - XY) + Z = TAN(PIE)

1- Z[(X + Y) /(1-XY)]

(X + Y / 1 - XY) + Z = 0

1- Z[(X + Y) /(1-XY)]

[(X + Y) / (1 - XY)] + Z = 0

(X + Y) / (1 - XY) = -Z

X + Y = -Z(1 - XY)

X + Y = -Z + XYZ

X + Y + Z = XYZ

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tan-1x+tan-1y+tan-1z=π -: tan-1(x+y/1-xy)+z=π. [tan-1x+tan-1y =(x+y/1-xy)] -: (x+y/1-xy)+z=tanπ -: (x+y/1-xy)+z=0 -: (x+y/1-xy)=-z -: x+y=-z(1-xy) -: x+y=-z+xyz Hence, x+y+z=xyz
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Tan ^-1 (1/rot x^2-1)
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X+y/1-xy=-z next step
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Very easy method :

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Process cannot be solved please check Solution
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