### Instruction: Express $\sin (a + b) - \sin (a - b)$ as the product of trigonometric functions.### Response: We can use the sum-to-product trigonometric identity, which says that $\sin x - \sin y = 2 \sin(\frac{x-y}{2}) \cos(\frac{x+y}{2})$.
In this case, $x = a+b$ and $y = a-b$.
So we have $\sin (a + b) - \sin (a - b) = 2 \sin(\frac{a+b-(a-b)}{2}) \cos(\frac{a+b+(a-b)}{2})$.