sinα+cosα=3根号55,α属于（0,π4）,
sin^2a+cos^2a=1
sina=√5/5,cosa=2√5/5
sin(β-π4)=35,β属于（π4,π2）
cos(β-π4)=4/5
sin(2β-π/2)=2sin(β-π/4)cos(β-π/4)=24/25=-cos(2β)
cos(2β)=-24/25,sin(2β)=7/25
sin2a=2sinacosa=4/5,tana=1/2
cos(α+2β)=cosacos(2β)-sinasin(2β)=-2√5/5*24/25-√5/5*7/25=-11√5/25