### Instruction: Express $\sin (a + b) - \sin (a - b)$ as the product of trigonometric functions.### Response: I recall that there are some formulas for the sine of a sum and difference of angles.
One of them is $\sin (a + b) = \sin a \cos b + \cos a \sin b$.
Another one is $\sin (a - b) = \sin a \cos b - \cos a \sin b$.
If I subtract these two formulas, I get $\sin (a + b) - \sin (a - b) = 2 \cos a \sin b$.
This is already the product of two trigonometric functions, so I am done.