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

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

Text Solution

Verified by Experts

`L.H.S->cos6x = cos(3(2x))`
We know, `cos3x = 4cos^3x-3cosx`
`cos(3(2x)) = 4cos^3(2x) - 3cos2x`
`=4(2cos^2x -1)^3 - 3(2cos^2x-1)`
`=4(8cos^6x-12cos^4x+6cos^2x-1)-6cos^2x+3`
`=32cos^6x -48cos^4x+18cos^2x-1 = R.H.S.`
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