Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 59

$\frac{3}{2}(\cos 11x+\cos 3x)$

Use the third Sum-to-Product Formula on page 559, $\cos u\cos v=\frac{1}{2}[\cos(u+v)+\cos(u-v)]$. $3\cos 4x\cos 7x$ $=3\times\frac{1}{2}[\cos(4x+7x)+\cos(4x-7x)]$ $=\frac{3}{2}[(\cos 11x+\cos (-3x)]$ $=\frac{3}{2}(\cos 11x+\cos 3x)$