Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 693: 47

$2\cos 6x\cdot\cos 2x$

Sum-to-Product: $\displaystyle \cos A+\cos B=2\cos(\frac{A+B}{2})\cos(\frac{A-B}{2})$ $\cos(-A)=\cos A$ ---------- $\displaystyle \frac{A+B}{2}=\frac{4x+8x}{2}=6x$ $\displaystyle \frac{A-B}{2}=\frac{4x-8x}{2}=-2x$ $\cos A+\cos B=2\cos 6x\cos(-2x)$ $= 2\cos 6x\cdot\cos 2x$