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Find the value of (cos^(2)66^(@)-sin^(2)...

Find the value of `(cos^(2)66^(@)-sin^(2)6^(@))(cos^(2)48^(@)-sin^(2)12^(@))`.

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(16)`
`(cos^(2)66^(@)-sin^(2)6^(@))(cos^(2)48^(@)-sin^(2)12^(@))`
`=(cos 72^(@).cos60^(@))(cos 60^(@).cos36^(@))`
`=(cos 60^(@))^(2).sin18^(@).cos36^(@)`
`=(1)/(4)((sqrt(5)-1)/(4))((sqrt(5)+1)/(4))`
`=(1)/(16)`
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