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Question
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
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Solution
sin26x – sin24x = (sin6x + sin4x) (sin 6x - sin 4x)
= `2sin ((6x + 4x)/2) cos ((6x - 4 x) /2) 2 sin ((6x - 4x)/2) cos ((6x + 4x)/2)`
= (2sin5x cosx) (2cos 5x sinx)
= (2sin x cos x)(2sin 5x cos5x)
= sin 2x sin 10x
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