α∈（π/2,π）且sinα=4/5
所以cosα=-3/5
sin(α+π/4)-√2/2cosα
=sinαcosπ/4＋cosαsinπ/4-√2/2cosα
=√2/2sinα＋√2/2cosα-√2/2cosα
=√2/2sinα
=√2/2 ×4/5
=2√2/5