Prove that sin20 sin40 sin60 sin80=3/16

Question

Mathematics

Alisha

6 July, 13:57

Prove that sin20 sin40 sin60 sin80=3/16

+2

Answers (1)

Know the Answer?

Gillian Todd · 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)