If $\tan ^{-1}(a / x)+\tan ^{-1}(b / x)=\pi / 2$, then $x$ is equal to

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

\tan ^{-1}(a / x)+\tan ^{-1}(b / x)=\pi / 2

, then

x

is equal to

View answer and explanation

Correct option: D

\sqrt{a b}

Option D,

\sqrt{ab}

, is correct because by applying the tangent addition formula and using the given condition, we can derive that

x = \sqrt{ab}

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