=cos²x-cos²y
=(1+cos2x)/2-(1+cos2y)/2
=(cos2x-cos2y)/2
={cos[(x+y)+(x-y)]-cos[(x+y)-(x-y)]}/2
=[cos(x+y)cos(x+y)-sin(x+y)sin(x-y)-cos(x+y)cos(x+y)-sin(x+y)sin(x-y)]/2
=-sin(x+y)sin(x-y)