由题意,tana=2或1/2,又a∈[π/4,π/2],tana>1,故tana=2
由万能公式,cos2a=1-tan^2 a/1+tan^2 a=1-4/1+4=3/5
sin2a=2tana/1+tan^2 a=4/5
sin(2a+π/4)=sin2a+cos2a=7/5