Chapter 7 - Trigonometric Identities and Equations - Chapter 7 Test Prep - Review Exercises - Page 736: 9

$\sec^{2}\theta$

$\displaystyle \frac{\sin^{2}\theta}{\cos^{2}\theta}(1+\frac{\cos^{2}\theta}{\sin^{2}\theta})=\frac{\sin^{2}\theta}{\cos^{2}\theta}+\frac{\sin^{2}\theta}{\cos^{2}\theta}\times\frac{\cos^{2}\theta}{\sin^{2}\theta}$ $=\displaystyle \frac{\sin^{2}\theta}{\cos^{2}\theta}+1$ $=\displaystyle \frac{\sin^{2}\theta+\cos^{2}\theta}{\cos^{2}\theta}$ $=\displaystyle \frac{1}{\cos^{2}\theta}$ $=(\displaystyle \frac{1}{\cos\theta})^{2}$ $=\sec^{2}\theta$