Prove that sin² 6x – sin² 4x = sin 2x sin 10x

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Solution

It is known that

∴L.H.S. = sin²6x – sin²4x

= (sin 6x + sin 4x) (sin 6x – sin 4x)

= (2 sin 5x cos x) (2 cos 5x sin x)

= (2 sin 5x cos 5x) (2 sin x cos x)

= sin 10x sin 2x

= R.H.S.

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