\(\displaystyle\Rightarrow{\left({r}{\cos{\theta}}\right)}{\left({r}{\sin{\theta}}\right)}={2}\)

\(\displaystyle{r}^{{{2}}}{\cos{\theta}}{\sin{\theta}}={2}\)

\(\displaystyle\Rightarrow{r}^{{{2}}}\cdot{\frac{{{\sin{{2}}}\theta}}{{{2}}}}={2}\)

\(\displaystyle\Rightarrow{r}^{{{2}}}\cdot{\sin{{2}}}\theta={4}\)

\(\displaystyle\Rightarrow{r}^{{{2}}}={\frac{{{4}}}{{{\sin{{2}}}\theta}}}\)

\(\displaystyle\Rightarrow{r}^{{{2}}}={4}{\csc{{2}}}\theta\)

\(\displaystyle{r}^{{{2}}}{\cos{\theta}}{\sin{\theta}}={2}\)

\(\displaystyle\Rightarrow{r}^{{{2}}}\cdot{\frac{{{\sin{{2}}}\theta}}{{{2}}}}={2}\)

\(\displaystyle\Rightarrow{r}^{{{2}}}\cdot{\sin{{2}}}\theta={4}\)

\(\displaystyle\Rightarrow{r}^{{{2}}}={\frac{{{4}}}{{{\sin{{2}}}\theta}}}\)

\(\displaystyle\Rightarrow{r}^{{{2}}}={4}{\csc{{2}}}\theta\)