若x∈(0,π/4),求函数y+cos²x-sin²x+2sinxcosx的值域

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=√2
再问： cos2x+sin2x怎么转化成√2sin(2x+π/4)
再答： cos2x+sin2x =√2* (√2/2cos2x+√2/2sin2x) =√2(sin2xcosπ/4+cos2xsinπ/4) =√2sin(2x+π/4) 值域为（1，√2】