sinα＋cosα=√2[(√2/2)sinα＋(√2/2)cosα]
=√2[sinαcos(π/4)＋cosαsin(π/4)]
=√2sin(α+π/4)
∵-1≤sin(α+π/4)≤1
∴-√2≤√2sin(α+π/4)≤√2
∴sinα＋cosα最大值是√2,最小值是-√2