y=2cos²x+sin2x
=1+cos2x+sin2x
=1+

2

(

2

2

cos2x+

2

2

sin2x)
=1+

2

sin(2x+

π

4

)
当2x+

π

4

=2kπ−

π

2

，有最小值1-

2

故答案为1-

2