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Prove that sin 12^(@) sin18^(@)sin42^(@)...

Prove that `sin 12^(@) sin18^(@)sin42^(@) sin48^(@) sin 72^(@) sin78^(@)=(cos18^(@))/(32)`.

Text Solution

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`sin 12^(@)sin18^(@)42^(@)sin48^(@)sin 72^(@)sin78^(@)`
`=(sin 12^(@)sin48^(@)sin72^(@))(sin18^(@)sin42^(@)sin78^(@))`
`=(1)/(4)sin 36^(@)(1)/(4)sin 54^(@)`
`=(1)/(16)sin36^(@)cos36^(@)`
`=(1)/(32)sin 72^(@)`
`=(cos 18^(@))/(32)`
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