Eduprobe
Question:
Prove that: sinx + sin3x + sin5x + sin7x = 4cosxcos2xsin4x
Solution:
LHS = sinx + sin3x + sin5x + sin7x
= sinx + sin7x + sin3x + sin5x
= 2sin4xcos3x + 2sin4xcosx
= 2sin4x(cos3x + cosx)
= 4sin4xcosxcos2x
= RHS
Hence proved