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Find the value of tan-1(xy)+tan-1(y-xy+x) - Mathematics

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Question

Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`

Sum

Solution

`tan^-1(x/y) + tan^-1((y - x)/(y + x))`

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

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

= `tan^-1(1)`

= `π/4`

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