सिद्ध कीजिए कि
`sin 12^(@) sin 48^(@) sin 54^(@) =1/8`

Explanation

` L.H.S = sin 12^(@) sin 48^(@) sin 54^(@) `
` 1/2 * ( 2 sin 48^(@) sin 12^(@)) * sin (90^(@)- 36^(@))`
` = 1/2 [ cos ( 48^(@)-12^(@))`
` - cos [(48^(@)+ 12^(@))] * cos 36^(@)`
` 1/2 [ cos 36^(@)- cos 60^(@)] * cos 36^(@)`
` = 1/2 [ (sqrt(5)+1)/4 - 1/2 ] * (( sqrt(5)+1)/4)`
` = 1/2 ( (sqrt(5)+1-2)/4)* ((sqrt(5)+1)/4)`
` = ((sqrt(5)-1)(sqrt(5)+1))/32 = (5-1)/32 = 4/32 `
` = 1/8 = R.H.S `