If tan-1x + tan-1y = π/4 than write the value of x + y + xy. – InterviewSolution

1.

If tan-1x + tan-1y = π/4 than write the value of x + y + xy.

Answer»

tan^-1x + tan^-1y = π/4

⇒ tan^-1((x + y)/(1 - x.y)) = π/4

⇒ (x + y)/(1 - x.y) = tan(π/4) = 1

⇒ x + y = 1 - xy ⇒ x + y + xy = 1

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