सिद्ध कीजिए कि
` sin 6^(@) sin 42^(@) sin 66^(@) sin 78^(@) =1/16`

Explanation

` L.H.S = sin 6^(@) sin 42^(@) sin 66^(@)sin 78^(@)`
` = 1/4 (2 sin 66^(@)sin6^(@)) *(2 sin 78^(@)sin 42^(@))`
` = 1/4 [ cos (66^(@)-6^(@))-cos(66^(@)+6^(@))]`
` [ cos (78^(@)- 42^(@))- cos (78^(@)+42^(@))] `
` = 1/4 [ cos 60^(2) - cos72^(@)][cos36^(2)- cos 120^(@)]`
` = 1/4 [ 1/2 - cos (90^(@)-18^(@)]`
` [ cos 36^(@)- cos(90^(@) - 18^(@))] `
` 1/4 [ 1/2 - sin 18^(@)] [ cos 36^(2)+ sin30^(@)]`
` = 1/4 [ 1/2 - (sqrt(5)-1)/4 ][(sqrt(5)+1)/4 +1/2]`
` = 1/4 [ (2-sqrt(5)+1)/4 ][(sqrt(5)+1+2)/4]`
` = ((3-sqrt(5))(3+sqrt(5)))/64 `
` = (9-5)/64 = 4/64 = 1/16 = R.H.S `