Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises - Page 37: 81

$1+\cot^{2}\theta=\csc^{2}\theta$

$\frac{x^{2}}{y^{2}}+\frac{y^{2}}{y^{2}}=\frac{r^{2}}{y^{2}}$ $(\frac{x}{y})^{2}+1=(\frac{r}{y})^{2}$ Substitute in trig functions $(\cot\theta)^{2}+1=(\csc\theta)^{2}$ $1+\cot^{2}\theta=\csc^{2}\theta$