解y=2cos^2x+sin2x-2
=2cos^2x-1+sin2x-1
=cos2x+sin2x-1
=√2（√2/2sin2x+√2/2cos2x）-1
=√2sin（2x+π/4)-1
≤√2-1
故y=2cos^2x+sin2x-2的最大值√2-1.