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in Mathematics by (128k points)
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Prove that cos22x – cos26x = sin 4x sin 8x

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Best answer

We know that

∴L.H.S. = cos2 2x – cos2 6x

= (cos 2x + cos 6x) (cos 2– 6x)

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

= (2 sin 4x cos 4x) (2 sin 2x cos 2x)

= sin 8x sin 4x

= R.H.S.

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