Prove that: (sin7x+sin5x)+(sin9x+sin3x)/(cos7x+cos5x)+(cos9x+cos3x)=tan6x

LHS=(sin7x+sin5x)+(sin9x+sin3x)/(cos7x+cos5x)+(cos9x+cos3x)
=2sin(7x+5x/2)cos(7x-5x/2)+2sin(9x+3x/2)cos(9x-3x/2)/2cos(7x+5x/2)cos(7x-5x/2)+2cos(9x+3x/2)cos(9x-3x/2)
=2sin(6x)cos(x)+2sin(6x)cos(3x)/2cos(6x)cos(x)+2cos(6x)cos(3x)
=2sin(6x)[cos(x)+cos(3x)]/2cos(6x)[cos(x)+cos(3x)]
=sin6x/cos6x
=tan6x
=RHS
Hence proved