### Instruction: Express $\sin (a + b) - \sin (a - b)$ as the product of trigonometric functions.### Response: I know that there are some formulas for the sum and difference of angles for sine and cosine, so I might try to use those here.
The formula for $\sin (a + b)$ is $\sin a \cos b + \cos a \sin b$, and the formula for $\sin (a - b)$ is $\sin a \cos b - \cos a \sin b$.
If I subtract these two expressions, I get $\sin (a + b) - \sin (a - b) = 2 \cos a \sin b$.
This is already a product of trigonometric functions, so I'm done.