## Functions Modeling Change: A Preparation for Calculus, 5th Edition

$$6\cos \left(t\right)\sin \left(t\right)-8sint$$
Simplifying the expression, we obtain: $$2\cos \left(t\right)\left(3\sin \left(t\right)-4\tan \left(t\right)\right)$$ Since tangent equals $\frac{sint}{cost}$, it follows: $$2\cdot \:3\cos \left(t\right)\sin \left(t\right)-2\cdot \:4\cos \left(t\right)\tan \left(t\right) \\ 6\cos \left(t\right)\sin \left(t\right)-8\cos \left(t\right)\tan \left(t\right) \\ 6\cos \left(t\right)\sin \left(t\right)-8sint$$