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

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

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Application +4 | -1

{\tan ^{ - 1}}x - {\tan ^{ - 1}}y = {\tan ^{ - 1}}A,\mathrm{then\;}A\mathrm{\;is\;equal\;to}

View answer and explanation

Correct option: C

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

Option C (

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

) is correct because it directly applies the tangent subtraction formula:

{\tan ^{ - 1}}x - {\tan ^{ - 1}}y = {\tan ^{ - 1}}\left( {\frac{{x - y}}{{1 + xy}}} \right)

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