cos(β-π/4)=1/3cos2(β-π/4)=2[cos(β-π/4)]^2-1=-7/9cos(2β-π/2)=-7/9cos(π/2-2β)=-7/9sin2β=-7/9cos(β-π/4)=1/3,sin(α+β)=4/5,0＜α＜π/2＜β＜πsin(β-π/4)=2√2/3cos(α+β)=-3/5cos(α+π/4)=c...