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Prove that:cos6x=32cos^6x-48cos^4x+18cos...

Prove that:`cos6x=32cos^6x-48cos^4x+18cos^2x-1`

Text Solution

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LHS `=cos6x`
`=cos3(2x)=4cos^(3)2x-3cos2x`
`cos2x[4(cos2x)^(2))-3]`
`=cos2x[4(2cos^(2)x-1)^(2)-3]`
`=(2cos^(2)x-1)(16cos^(4)x-16cos^(2)x+1)`
`32cos^(6)x-32cos^(4)x+2cos^(2)-16cos^(4)x+16cos^(2)x-1`
`=32cos^(6)x-48cos^(4)x+18cos^(2)-1` = R.H.S Hence Proved.
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