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Question

Question: If ![](https://cdn.pureessence.tech/canvas_213.png?top_left_x=300&top_left_y=1675&width=300&height=4...

If then A =

A

x−yx - y

B

x+yx + y

C

x−y1+xy\frac { x - y } { 1 + x y }

D

x+y1−xy\frac { x + y } { 1 - x y }

Answer

x−y1+xy\frac { x - y } { 1 + x y }

Explanation

Solution

Given that tan⁡−1x−tan⁡−1y=tan⁡−1A\tan ^ { - 1 } x - \tan ^ { - 1 } y = \tan ^ { - 1 } A

⇒tan⁡−1(x−y1+xy)=tan⁡−1A\Rightarrow \tan ^ { - 1 } \left( \frac { x - y } { 1 + x y } \right) = \tan ^ { - 1 } A.

Hence A=x−y1+xyA = \frac { x - y } { 1 + x y }.