Step 1: Use the sum-to-product identity for sine. The identity is $\sin A + \sin B = 2 \sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)$. Step 2: Substitute $A = 50^\circ$ and $B = 30^\circ$ into the identity. $$ \sin 50^\circ + \sin 30^\circ = 2 \sin \left(\frac{50^\circ+30^\circ}{2}\right) \cos \left(\frac{50^\circ-30^\circ}{2}\right) $$ Step 3: Simplify the angles. $$ \sin 50^\circ + \sin 30^\circ = 2 \sin \left(\frac{80^\circ}{2}\right) \cos \left(\frac{20^\circ}{2}\right) $$ $$ \sin 50^\circ + \sin 30^\circ = 2 \sin 40^\circ \cos 10^\circ $$ The expression as a product is: $$ \boxed{2 \sin 40^\circ \cos 10^\circ} $$ Send me the next one 📸