Simplify $\sin (x - y) \cos y + \cos (x - y) \sin y.$
From the angle addition formula, the expression is equal to $\sin ((x - y) + y) = \boxed{\sin x}.$
From the angle addition formula, the expression is equal to $\sin ((x - y) + y) = \boxed{\sin x}.$
The final answer is $$\sin x$$. I hope it is correct.