Express $\sin (a + b) - \sin (a - b)$ as the product of trigonometric functions.
By sum-to-product,
\[\sin (a + b) - \sin (a - b) = \boxed{2 \sin b \cos a}.\]
By sum-to-product,
\[\sin (a + b) - \sin (a - b) = \boxed{2 \sin b \cos a}.\]
The final answer is $\(2 \sin b \cos a\)$. I hope it is correct.