Chapter 9 - Trigonometric Identities, Models, and Complex Numbers - 9.2 Identities, Expressions, and Equations - Exercises and Problems for Section 9.2 - Exercises and Problems - Page 363: 11

$$\cos \left(t\right)+3\sin \left(t\right)$$

Simplifying the expression, we obtain: $$2\cos \left(t\right)-\cos \left(t\right)+3\cos \left(t\right)\tan \left(t\right)$$ Since tangent equals $\frac{sint}{cost}$, it follows: $$\cos \left(t\right)+3\cos \left(t\right)\tan \left(t\right)\\ \cos \left(t\right)+3\cos \left(t\right)\frac{\sin \left(t\right)}{\cos \left(t\right)} \\ \cos \left(t\right)+3\sin \left(t\right)$$