Answer
The rectangular equation is, $xy=1$
Work Step by Step
Using, $r\cos \theta =x$, and $r\sin \theta =y$ we will convert the polar equation to the rectangular equation.
Therefore,
$\begin{align}
& {{r}^{2}}\sin 2\theta =2 \\
& 2{{r}^{2}}\sin \theta \cos \theta =2 \\
& r\sin \theta \times r\cos \theta =1 \\
& xy=1
\end{align}$
Hence, the rectangular equation of ${{r}^{2}}\sin 2\theta =2$ is $xy=1$.
