1. The problem is to simplify the expression $\cos 60\cos 30 + \sin 60\sin 30$.\n\n2. Recognize that this expression matches the cosine addition formula: $$\cos(a - b) = \cos a \cos b + \sin a \sin b$$\n\n3. Here, $a = 60^\circ$ and $b = 30^\circ$, so the expression simplifies to: $$\cos(60^\circ - 30^\circ)$$\n\n4. Calculate the inside of the cosine: $$60^\circ - 30^\circ = 30^\circ$$\n\n5. Evaluate $\cos 30^\circ$. Using known values, $$\cos 30^\circ = \frac{\sqrt{3}}{2}$$\n\n6. Therefore, the expression simplifies to $$\frac{\sqrt{3}}{2}$$\n\n7. Final answer: $$\cos 60\cos 30 + \sin 60 \sin 30 = \frac{\sqrt{3}}{2}$$