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Question:

Prove the following: cos9x - cos5xsin17x - sin3x = -sin2xcos10x

Solution:

LHS=cos9x - cos5xsin17x - sin3x = -2sin(9x+5x/2)sin(9x-5x/2)/2cos(17x+3x/2)sin(17x-3x/2) = -sin7xsin2xcos10xsin7x = -sin2xcos10x = RHS
Hence proved