Prove the following: cot4x(sin5x+sin3x)=cotx(sin5x-sin3x)

LHS=cot4x(sin5x+sin3x)=cos4x/sin4x[2sin((5x+3x)/2)cos((5x-3x)/2)]=cos4x/sin4x[2sin(4x)cos(x)]=2cos4xcosx/sin4x=cosx/sinx(2cos4xsinx)=cotx(sin5x-sin3x)Hence proved