सिध्द कीजिए कि : `sin alpha sin (60^(@) – alpha) sin (60^(@)+ alpha) = (1)/(4) sin 3 alpha`

Explanation

दायाँ पक्ष `= (1)/(4) sin 3 alpha `
`=(1)/(4) [ 3 sin alpha – 4 sin^(3) alpha] = (sin alpha)/(2) [ (3)/(2)- 2 sin^() alpha]`
` = (sin alpha)/(2)[ 1-2 sin^(2) alpha+ (1)/(2) ] = (sin alpha)/(2) [ cos 2 alpha + (1)/(2)]`
`= (sin alpha)/(2)[ cos 2 alpha - cos 120^(@)]`
`=(sin alpha)/(2)[ 2 sin ((2alpha + 120^(@))/(2)) sin .((120^(@) - 2 alpha)/(2)) ]`
`= sin alpha sin (60^(@)+ alpha ) sin (60^(@) - alpha)`
`=` बायाँ पक्ष।