解
y=√2cos²x-√2sin²x+2√2sinxcosx+1
=√2(cos²x-sin²x)+√2sin2x+1
=√2sin2x+√2cos2x+1
=2(√2/2sin2x+√2/2cos2x)+1
=2(sin2xcosπ/4+cos2xsinπ/4)+1
=2sin(2x+π/4)+1
∵sin(2x+π/4)∈[-1,1]
∴-1