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Prove that:

cos20°cos40°cos80°=1/8​

2 Answers

6 votes

Explanation:

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Prove that: cos20°cos40°cos80°=1/8​-example-1
User Chejaras
by
6.7k points
5 votes

Answer:

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

User Jspboix
by
8.2k points