sinx+siny=1
(sinx+siny)^2=1
sinx^2+siny^2+2sinxsiny=1
sinx^2+siny^2=1-2sinxsiny
(cosx+cosy)^2=cosx^2+cosy^2+2cosxcosy
=1-sinx^2+1-siny^2+2cosxcosy
=2-(sinx^2+siny^2)+2cosxcosy
=2-(1-2sinxsiny)+2cosxcosy
=1+2(sinxsiny+cosxcosy)
=1+2cos(x-y)
当x=y时取最大值 sinx=siny=1/2时
最大值为3