Prove that cos² 2x – cos² 6x = sin 4x sin 8x

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Solution

It is known that

∴L.H.S. = cos² 2x – cos² 6x

= (cos 2x + cos 6x) (cos 2x – 6x)

= [2 cos 4x cos 2x] [–2 sin 4x (–sin 2x)]

= (2 sin 4x cos 4x) (2 sin 2x cos 2x)

= sin 8x sin 4x

= R.H.S.

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