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Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x.

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Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x.

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LHS = 1 + cos 2x + cos 4x + cos 6x 

= (1 + cos 6x) + (cos 2x + cos 4x) 

= 2cos2 3x + 2cos 3x cos x 

= 2 cos 3x (cos 3x + cos x)

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