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Prove that: sin12^(@)sin48^(@)sin54^(@...

Prove that:
`sin12^(@)sin48^(@)sin54^(@)=1/8`

Text Solution

Verified by Experts

We have,
`sin 12^(@).sin48^(@).sin54^(@)`
`=1/2 (2sin12^(@).sin48^(@)).sin(90^(@)-36^(@))`
`=1/2 [cos36^(@)-cos60^(@)].cos36^(@)` [using `sin(90^(@)-theta)=costheta`]
`=1/2[cos36^(@)-1/2].cos 36^(@)`
`1/2[(sqrt(5)+1)/(4) -1/2].((sqrt(5)+1)/(4))`
`=1/2(5-1)/(16)`
`=1/8`
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