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Prove that: cos18^0-sin18^0 = sqrt(2)sin...

Prove that: `cos18^0-sin18^0 = sqrt(2)sin27^0`

Text Solution

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LHS`=cos18^(@)-sin18^(@)`
`=cos18^(@)-sin(90^(@)-72^(@))=cos18^(@)-cos72^(@)`
`=sin(18^(@)+72^(2))/(2)sin(72^(@)-18^(@))/(2)`
`=sin 45^(@)sin27^(@)`
`=2(1)/sqrt(2)sin27^(@)`
`=sqrt(2) sin 27^(@)`.
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