1. We are asked to simplify the expression $\sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ$. 2. Recall that this matches the sine addition formula: $\sin(a+b) = \sin a \cos b + \cos a \sin b$. 3. Here, $a = 60^\circ$ and $b = 30^\circ$, so the expression equals $\sin(60^\circ + 30^\circ) = \sin 90^\circ$. 4. We know $\sin 90^\circ = 1$. 5. Therefore, $\sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ = 1$. Final answer: $1$