Given that Sin x - sin y =p and cos x +cos y=q Express cos (x+y ) in terms of p and q?

Sol
Sinx－Siny=p
Sin^2 x－2SinxSiny+Sin^2 y=p^2
Cosx+Cosy=q
Cos^2 x+2CosxCosy+Cos^2 y=q^2
q^2+p^2
=(Cos^2 x+2CosxCosy+Cos^2 y)+(Sin^2 x－2SinxSiny+Sin^2 y)
=2+2Cos(x+y)
Cos(x+y)=(p^2+q^2－2)/2