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Question
Prove the following:
cos2 2x – cos2 6x = sin 4x sin 8x
Solution
cos2 2x – cos2 6x = (cos2x + cos6x) (cos 2x - cos 6x)
= `2cos ((2x + 6x)/2) cos ((2x - 6 x) /2) - 2sin ((2x - 6x)/2) sin ((2x + 6x)/2)`
= (2cos 4x cos2x) (2sin 4x sin 2x)
= (2sin 2x cos2x)(2sin 4x cos4x) = sin 4x sin 8x
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