y=cos²x-sin²x+2sinxcosx=cos2x+sin2x=√2sin(2x+π/4)
所以
x=0或π/4时取最小值=1
x=π/8时取最大值=√2cos2x+sin2x怎么转化成√2sin(2x+π/4)cos2x+sin2x=√2* (√2/2cos2x+√2/2sin2x)=√2(sin2xcosπ/4+cos2xsinπ/4)=√2sin(2x+π/4)值域为（1，√2】