Prove that sin20 sin40 sin60 sin80=3/16

Question

Rebecca Schwartz

Mathematics

26 January, 07:47

Prove that sin20 sin40 sin60 sin80=3/16

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Amos · 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)