If cot^{-1} alpha + cot^{-1} beta = cot^{-1} | vedclass

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Question

(D) We are given the equation $\cot^{-1} \alpha + \cot^{-1} \beta = \cot^{-1} x$.Using the standard identity for the sum of inverse cotangent function

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) We are given the equation $\cot^{-1} \alpha + \cot^{-1} \beta = \cot^{-1} x$.Using the standard identity for the sum of inverse cotangent functions,$\cot^{-1} \alpha + \cot^{-1} \beta = \cot^{-1} \left( \frac{\alpha \beta - 1}{\alpha + \beta} \right)$.Comparing this with the given equation $\cot^{-1} x$,we get $x = \frac{\alpha \beta - 1}{\alpha + \beta}$.Thus,the correct option is $D$.

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

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