(1).由正切的半角公式知2tana=1.===>tana=1/2.===>sin2a=4/5,cos2a=3/5.(2)3sinb=sin(2a+b)=sin2acosb+cos2asinb=(4/5)cosb+(3/5)sinb.===>tanb=1/3.(3)tan(a+b)=[tana+tanb]/(1-tanatanb)=1.===>a+b=π/4.