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

Question

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