已知0＜α＜π/2＜β＜π,cos（β-π/4π）=1/3,sin（α+β）=4/5,sin2β=-7/9.cos(α+π/4)的值
问题描述：
已知0＜α＜π/2＜β＜π,cos（β-π/4π）=1/3,sin（α+β）=4/5,sin2β=-7/9.cos(α+π/4)的值
答
cos(β-π/4)=1/3 cos2(β-π/4)=2[cos(β-π/4)]^2-1=-7/9 cos(2β-π/2)=-7/9 cos(π/2-2β)=-7/9 sin2β=-7/9 cos(β-π/4)=1/3,sin(α+β)=4/5,0＜α＜π/2＜β＜π sin(β-π/4)=2√2/3 cos(α+β)=-3/5 cos(α...