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Q)

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

$\begin{array}{1 1}(a)\;\sqrt{ab}&(b)\;\sqrt{2ab}\\(c)\;2ab&(d)\;ab\end{array}$

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A)
$\tan^{-1}\big(\large\frac{a}{x}\big)$$+\tan^{-1}\big(\large\frac{b}{x}\big)=\large\frac{\pi}{2}$
$\tan^{-1}\big(\large\frac{a}{x}\big)$$+\cot^{-1}\big(\large\frac{x}{b}\big)=\frac{\pi}{2}$
$\large\frac{a}{x}=\frac{x}{b}$
$x^2=ab$
$x=\pm\sqrt{ab}$
Hence (d) is the correct option.
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