Answer
See the answer below.
Work Step by Step
$x^{2}+y^{2}=r^{2}$
Dividing by $y^{2}$, we get
$\frac{x^{2}}{y^{2}}+\frac{y^{2}}{y^{2}}=\frac{r^{2}}{y^{2}}$
Or $(\frac{x}{y})^{2}+1=(\frac{r}{y})^{2}$
Knowing that $\frac{x}{y}=\cot\theta$ and $\frac{r}{y}=\csc\theta$, we obtain
$1+\cot^{2}\theta=\csc^{2}\theta$
