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Prove that:cos^2 2x-cos^2 6x=sin4xsin8x...

Prove that:`cos^2 2x-cos^2 6x=sin4xsin8x`

Text Solution

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LHS `=cos^(2)2x-cos^(2)6x`
`=1/2[2cos^(2)2x-2cos^(2)6x]`
`=1/2[cos4x-cos12x]`
`=1/2[2sin(4x+12x)/(2)sin(12x-4x)/(2)]`
`=sin8xsin4x=sin4xsin8x` = R.H.S. Hence Proved.
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