Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 666: 37

$\tan^2 \beta$

$\frac{\sin\beta\tan\beta}{\cos \beta}$ $=\frac{\sin\beta*\frac{\sin\beta}{cos \beta}}{\cos \beta}$ $=\frac{\frac{\sin^2\beta}{\cos\beta}}{\cos \beta}$ $=\frac{\sin^2\beta}{\cos^2\beta}$ $=(\frac{\sin\beta}{\cos \beta})^2$ $=\tan^2 \beta$