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Question:

Prove the following: sin5x + sin3x / cos5x + cos3x = tan4x

Solution:

LHS = sin5x + sin3x / cos5x + cos3x
= 2sin((5x+3x)/2)cos((5x-3x)/2) / 2cos((5x+3x)/2)cos((5x-3x)/2)
= tan4x
= RHS
Hence proved.