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Question
Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
Solution
4 cos x cos 2x . cos 3x = 4 cos x . cos 3x . cos 2x
= 4 cos x . [cos (3x + 2x) + cos (3x – 2x)]
2 cos x . [cos 5x + cos x] = 2 cos 5x . cos x + 2 cos2x
= 2 × `1/2` [cos (5x + x) + cos (5x – x)] + 1 + cos 2x
= cos 6x + cos 4x + 1 + cos 2x
= 1 + cos 2x + cos 4x + cos 6x
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