Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 208: 37

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

$$A=\frac{\sin\beta\tan\beta}{\cos\beta}$$ $$A=\Bigg(\frac{\sin\beta}{\cos\beta}\Bigg)\tan\beta$$ - Quotient Identity: $$\frac{\sin\beta}{\cos\beta}=\tan\beta$$ Apply to $A$: $$A=\tan\beta\tan\beta$$ $$A=\tan^2\beta$$