∵tanα=3 ==>sinα=3cosα==>(3cosα)^2+(cosα)^2=1==>(cosα)^2=1/10∴sin(2α+π/4)=sin(2α)cos(π/4)+cos(2α)sin(π/4) (应用和角公式)=2sinαcosα/√2+((cosα)^2-(sinα)^2)/√2 (应用倍角公式)=3√2(cos...