y=2sinx^2+2cosx-3
=2(1-cosx^2)+2cosx-3
=2-2cosx^2+2cosx-3
=-2cosx^2+2cosx-1
=-2(cosx^2-cosx+1/4)-1/2
=-2(cosx-1/2)^2-1/2
所以当cosx=1/2时,最大值为-1/2