Sin^2x+sin^2y+cos (x+y)cos (x-y)
Sin²x+sin²y+2cos(x+y+x-y)/2*cos(x+y-x+y)/2= =sin²x+sin²y+1/2(cosx(x+y-x+y)+cos(x+y+x-y))= =sin²x+sin²y+1/2(cos2x+cos2y)=sin²x+sin²y+1/2-sin²x+1/2-sin²y=1