Prove that :

cos 30°. cos 60° - sin 30°. sin 60° = 0

cos 30°. cos 60° - sin 30°. sin 60° = 0

L.H.S. = cos 30°. cos 60° - sin 30°. sin 60°

$= \dfrac{\sqrt3}{2} \times \dfrac{1}{2} - \dfrac{1}{2} \times \dfrac{\sqrt3}{2} \\[1em] = \dfrac{\sqrt3}{4} - \dfrac{\sqrt3}{4}\\[1em] = 0$

R.H.S. = 0

∴ L.H.S. = R.H.S.

Hence proved, cos 30°. cos 60° - sin 30°. sin 60° = 0.