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Class-12-science»Maths

tan -1 x + tan-1 y + tan -1 z=pi/2 show that xy+yz+zx=1

\tan^{- 1} x + \tan^{- 1} y + \tan^{- 1} z = \frac{π}{2} \Rightarrow \tan^{- 1} (\frac{x + y}{1 - xy}) + \tan^{- 1} z = \frac{π}{2} \Rightarrow \tan^{- 1} (\frac{\frac{x + y}{1 - xy} + z}{1 - (\frac{x + y}{1 - xy}) z}) = \frac{π}{2} \Rightarrow \frac{x + y + z - xyz}{1 - xy - xz - yz} = \tan (\frac{π}{2}) \Rightarrow \frac{x + y + z - xyz}{1 - xy - xz - yz} = \infty \Rightarrow \frac{x + y + z - xyz}{1 - xy - xz - yz} = \frac{1}{0} \Rightarrow 1 - xy - xz - yz = 0 \Rightarrow xy + yz + zx = 1

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