# Prove that cos20.cos40.cos80=1/8

1
by jee7v5icoopuni

2016-02-29T22:52:21+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
cos20.cos40.cos80 / 1
Multiplying Both Numerator And Denominator by 2Sin20

cos20.cos40.cos80⇒(2Sin20.cos20).cos40.cos80
---------------------------------------
2Sin20
⇒sin(2 * 20).cos40.cos80     [2SinA.CosA = Sin 2A]
--------------------------------                     ↓
2sin20

⇒sin40.cos40.cos80            You Would Know This
--------------------------            If u  Are In 11th or 12th
2sin20

[Multiplying both the numerator and denominator by 2]
⇒(2Sin40.Cos40).cos80
-----------------------------     [2SinA.CosA = Sin 2A]
2 * 2sin20

⇒Sin(2 * 40).cos80
----------------------
4Sin20

⇒  Sin80.cos80
------------------
4Sin20

[Multiplying both the numerator and denominator by 2]
⇒2*Sin80.cos80
---------------------               [2SinA.CosA = Sin 2A]
2  *  4Sin20

⇒Sin(2 * 80)
--------------
8 Sin 20

⇒Sin 160
-----------
8 Sin20
⇒Sin (180 -20)
-----------------       [Sin(180 - A) = Sin A]
8 SIn 20
⇒Sin 20 / 8 Sin 20
⇒1/8