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Question

Question: \[\cos 20{^\circ}\cos 40{^\circ}\cos 80{^\circ} =\]...

cos⁡20∘cos⁡40∘cos⁡80∘=\cos 20{^\circ}\cos 40{^\circ}\cos 80{^\circ} =

A

1/2

B

1/4

C

1/6

D

1/8

Answer

1/8

Explanation

Solution

cos⁡20ocos⁡40ocos⁡80o=sin⁡2320o23sin⁡20o=sin⁡160o8sin⁡20o=18\cos 20^{o}\cos 40^{o}\cos 80^{o} = \frac{\sin 2^{3}20^{o}}{2^{3}\sin 20^{o}} = \frac{\sin 160^{o}}{8\sin 20^{o}} = \frac{1}{8}.