### Instruction: Express $\sin (a + b) - \sin (a - b)$ as the product of trigonometric functions.### Response: To simplify this expression, I will use the addition and subtraction formulas for sine, which are $\sin (a + b) = \sin a \cos b + \cos a \sin b$ and $\sin (a - b) = \sin a \cos b - \cos a \sin b$.
Substituting these formulas into the original expression, I get $\sin (a + b) - \sin (a - b) = (\sin a \cos b + \cos a \sin b) - (\sin a \cos b - \cos a \sin b)$.
To simplify further, I will use the distributive property and combine like terms.
This gives me $\sin (a + b) - \sin (a - b) = 2 \cos a \sin b$.
I have now expressed the original expression as the product of two trigonometric functions, namely $\cos a$ and $\sin b$.