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Question:

Prove the following: cos22x - cos26x = sin4xsin8x

Solution:

LHS = cos22x - cos26x = (cos2x - cos6x)(cos2x + cos6x) = (2sin(2x+6x)/2 sin(6x-2x)/2)(2cos(2x+6x)/2 cos(6x-2x)/2) = (2sin4xcos4x)(2cos2xsin2x) = sin8xsin4x