Prove that :

sin 60° cos 30° + cos 60°. sin 30° = 1

sin 60° cos 30° + cos 60°. sin 30° = 1

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

$= \dfrac{\sqrt3}{2} \times \dfrac{\sqrt3}{2} + \dfrac{1}{2} \times \dfrac{1}{2} \\[1em] = \dfrac{3}{4} + \dfrac{1}{4}\\[1em] = \dfrac{3 + 1}{4}\\[1em] = \dfrac{4}{4}\\[1em] = 1$

R.H.S = 1

∴ L.H.S = R.H.S

Hence proved, sin 60° cos 30° + cos 60°. sin 30° = 1.