prove that sin x+sin3x+sin5x+sin7x=4cosx cos2x sin 4x

sinx+sin3x+sin5x+sin7x

(sin 3x + sin 5x) + (sin 7x + sin x )

2 sin 4x . cos x + 2 sin 4x . cos 3x

2 sin 4x (cos x+ cos 3x)

2 sin 4x (2 cos 2x . cos x)

2 cos 2x . cos x . sin 4x

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