If ^ -1 x- ^ -1 y= ^ -1 A, then A = - Vidyadip

MCQ

If $\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1} A$, then $A =$

A
$x-y$
B
$x+y$
✓
$\frac{x-y}{1+x y}$
D
$\frac{x+y}{1-x y}$

✓

Answer

Correct option: C.

$\frac{x-y}{1+x y}$

(C) $\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1} A$
$\Rightarrow \tan ^{-1}\left(\frac{x-y}{1+x y}\right)=\tan ^{-1} A$
$\Rightarrow A =\frac{x-y}{1+x y}$

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