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If xy < 1, ^{ -1 }{ x } + ^{ -1 }{ y } = _______.

Question

If $x y < 1$ , $tan^{- 1} x + tan^{- 1} y =$ _______.

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Charlotte Discussed

x y < 1

tan^{- 1} x + tan^{- 1} y =

_______.

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Text solutionVerified

Let

θ = tan^{- 1} x + tan^{- 1} y

Taking

tan

on both sides,

tan θ

= tan (tan^{- 1} x + tan^{- 1} y) = \frac{tan ( tan ^{- 1} x ) + tan ( tan ^{- 1} y )}{1 - tan ( tan ^{- 1} x ) tan ( tan ^{- 1} y )} = \frac{x + y}{1 - x y}

Therefore,

θ = tan^{- 1} (\frac{x + y}{1 - x y})

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