If $\cot ^{-1} \alpha+\cot ^{-1} \beta=\cot ^{-1} x$, then $x$ is equal to

$\frac{1+\alpha \beta}{\alpha+\beta}$

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

\cot ^{-1} \alpha+\cot ^{-1} \beta=\cot ^{-1} x

, then

x

is equal to

View answer and explanation

Correct option: D

\frac{\alpha \beta-1}{\alpha+\beta}

Option D (

\frac{{\alpha \beta-1}}{{\alpha+\beta}}

) is correct because it is derived from the cotangent addition formula applied to the given equation.

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