答案：3
∵tanα=1/2
∴tan2α=2tanα/(1-tanα^2)=4/3
∴sinα/cosα=1/2
sinα^2=1/5,cosα^2=4/5
(sinα+cosα)^2/cos2α
=(1+sin2α)/cos2α
=1/(cosα^2-sinα^2)+tan2α
=1/(4/5-1/5)+4/3
=5/3+4/3
=3