Question

Prove that:

cos20°cos40°cos80°=1/8​

Answer 1

Explanation:

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Answer 2

see explanation

Explanation:

Using the double angle identity for sine

sin2x = 2sinxcosx

Consider left side

cos20°cos40°cos80°

=
`(1)/(2sin20)` (2sin20°cos20°)cos40°cos80°

=
`(1)/(4sin20)` (2sin40°cos40°)cos80°

=
`(1)/(4sin20)` (sin80°cos80° )

=
`(1)/(8sin20)` (2sin80°cos80° )

=
`(1)/(8sin20)` . sin160°

=
`(1)/(8sin20)` . sin(180 - 20)°

=
`(1)/(8sin20)` . sin20°

=
`(1)/(8)` = right side , thus proven