Question

Prove that: `s in 12^0s in 48^0s in 54^0=1/8dot`

Answer 1

L.H.S. `=1/2[cos36^(@)-cos60^(@)]sin54^(2)=1/2[cos36^(@)sin54^(@)-1/2sin54^(@)]`
`=1/4[2cos36^(@)sin54^(@)-sin54^(@)]=1/4[sin90^(@)+sin18^(@)-sin54^(@)]`
`=1/4[1-(sin54^(@)-sin18^(@))]=1/4[1-2sin18^(@)cos36^(@)]`
`=1/4[1-(2sin18^(@))/(cos 18^(@)) cos36^(@)]=1/4[1-(sin 72^(@))/(2sin72^(@))]=1/4[1-1/2]=1/8` = RHS