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

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1} A

, and

x y>-1

, then

A

View answer and explanation

Correct option: C

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

Option C (

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

) is correct because using the tangent subtraction formula,

\tan^{-1} x - \tan^{-1} y = \tan^{-1} \frac{x-y}{1+xy}

, which directly gives the value of A.

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