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If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy. - Mathematics

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

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Solution

Here, `tan^(−1) x+tan^(−1) y=π/4, xy < 1.`

`tan^(-1)((x+y)/(1-xy))=pi/4`

`(x+y)/(1−xy)=1`

`x+y=1−xy`

`x+y+xy=1`

Therefore, the value of x + y + xy is 1.

 

Concept: Inverse Trigonometric Functions (Simplification and Examples)
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