sinθ+cosθ=√2sin(θ+π/4)
∵0＜θ＜π/2
∴π/4＜θ+π/4＜3π/4
√2 /2＜sin(θ+π/4)≤1
∴1＜√2sin(θ+π/4)≤√2
即：1＜sinθ+cosθ≤√2