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Prove that:  sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

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Proof of for the question is :

LHS= sin x+sin 3x+sin 5x+sin 7x = (sinx+sin 7x)+(sin 5x+sin 3x) =2 sin 4x.cos x+sin 4x.cos 3x =2 sin 4x[cos 3x+cos x] =2 sin 4x[2 cos 2x+cos x] =4 sin 4x.cos2x.cos x    hence proved


 2nd solution

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