Prove that `tan^(-1)(x/y)- tan^(-1)((x-y)/(x+y)) ` is ` (pi)/4` and No – InterviewSolution

InterviewSolution

1.	Prove that `tan^(-1)(x/y)- tan^(-1)((x-y)/(x+y)) ` is ` (pi)/4` and Not `(-3pi)/4` .
Answer» `tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))` `tan^(-1)((x/y)-((x-y)/(x+y)))/((x/y)*((x-y)/(x+y))` `tan^(-1)((x^2+xy-xy+y^2)/(xy+y^2+x^2-xy))` `tan^(-1)((x^2+y^2)/(x^2+y^2))` `tan^(-1)(1)` `pi/4`.

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