Simplify: tan-1(x/y) - tan-1((x - y)/(x + y)) – InterviewSolution

1.

Simplify: tan-1(x/y) - tan-1((x - y)/(x + y))

Answer»

Given tan^-1(x/y) - tan^-1((x - y)/(x + y)) = tan^-1(x/y) - tan^-1((x/y - 1)/(x/y + 1))

= tan^-1(x/y) - (tan^-1(x/y) - tan^-1) (∵ tan^-1x - tan^-1y = tan^-1((x - y)/(1 + x.y)))

tan^-11 = π/4

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