Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 66

$2\sin\frac{7x}{2}\cos\frac{x}{2}$

Use the first Sum-to-Product Formula, $\sin x+\sin y=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}$. $\sin3x+\sin 4x$ $=2\sin\frac{3x+4x}{2}\cos\frac{3x-4x}{2}$ $=2\sin\frac{7x}{2}\cos\frac{-x}{2}$ $=2\sin\frac{7x}{2}\cos\frac{x}{2}$