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Prove that: cos² 2x - cos² 6x = sin 4x sin 8x

Solution

Using sin²x +cos²x=1

cos² 2x - cos² 6x

={1-sin²2x}-{1-sin² 6x}

= sin² 6x- sin² 2x= sin(6x+2x) sin(6x-2x)

=sin 8x sin 4x