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Question
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
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Solution
sin x + sin 2x + sin 3x = sin x + 2 sin x cos x + 3 sin x – 4 sin3 x
= sin x [1 + 2 cos x + 3 – 4 sin2 x]
= sin x [2 cos x + 4 – 4 sin2 x ]
= sin x [2 cosx + 4(1 – sin2x)]
= sin x [2 cos x + 4 cos2x]
= 2 sin x cos x [1 + 2 cos x]
= sin 2x (1 + 2 cosx)
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