Question

Prove that sin20 sin40 sin60 sin80=3/16

Answer 1

sin 20° · sin 40° · sin 80° = 1/2 ( cos 20° - cos 60° ) · sin 80° =
= 1/2 ( cos 20° sin 80° - cos 60° sin 80° ) =
= 1/2 ( (sin 100° + sin 60°)/2 - 1/2 sin 80° )= ( sin 100° = sin 80° )
= 1/2 · ( 1/2 sin 60° ) = 1/4 sin 60° = √3 / 8
sin 60° = √ 3/2
√ 3 / 2 · √ 3 / 8 = 3/16 ( correct )