Prove that:
(sin7x+sin5x)+(sin9x+sin3x)(cos7x+cos5x)+(cos9x+cos3x)=tan6x
LHS=(sin7x+sin5x)+(sin9x+sin3x)(cos7x+cos5x)+(cos9x+cos3x)=2sin(7x+5x2)cos(7x−5x2)+2sin(9x+3x2)cos(9x−3x2)2cos(7x+5x2)cos(7x−5x2)+2cos(9x+3x2)cos(9x−3x2)
=sin6xcosx+sin6xcos3xcos6xcosx+cos6xcos3x=tan6x=RHS
Hence proved