a∈(0,π/2),tana=1/2,则tan2a=[2tana]/[1－tan²a]=4/3；sin(2a＋π/3)=(1/2)sin2a＋(√3/2)cos2a.sin2a=[2tana]/[1＋tan²a]=4/5,cos2a=[1－tan²a]/[1＋tan²a]=3/5,则sin(2a＋π/3)=(4＋3√3)/10