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  4. If tan -1 x- tan -1 y= tan -1 A, then A is equal to

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Q. If $\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1} A$, then $A$ is equal to

Inverse Trigonometric Functions

Solution:

Given that, $\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1} A$
$\Rightarrow \tan ^{-1}\left(\frac{ x - y }{1+ xy }\right)=\tan ^{-1} A $
$\therefore A =\frac{ x - y }{1+ xy }$