सिद्ध कीजिए कि
` cos 20^(@) cos 40^(@) cos 80^(@) = 1/8`

Explanation

` L.H.S = cos 20^(@) cos 40^(@) cos 80^(@) `
` 1/2 cos 20^(@) [ 2 cos 80^(@) cos 40^(@)]`
` = 1/2 cos 20^(@) [ cos (80^(@) +40^(@))+cos (80^(@)- 40^(@))] `
` = 1/2 cos 20^(@) [ cos (90^(@) + 30^(@)) + cos 40^(@)]`
` = 1/2 [ -sin 30^(@) cos 20^(@) + 1/2 * 2 cos 40^(@) cos 20^(@)]`
` = 1/2 [ -1/2 cos 20^(@) + 1/2 { cos ( 40^(@) + 20^(@)) + cos (40^(@) - 20^(@))}]`
` = 1/4 [ - cos 20^(@) + cos 60^(@) + cos 20^(@)] `
` = 1/4 xx cos60^(@) = 1/4 xx 1/2 = 1/8 `
= R.H.S