∵sinα+cosα=1/5 ==>(sinα+cosα)²=1/25
==>sin²α+cos²α+2sinαcosα=1/25
==>1+sin(2α)=1/25
∴sin(2α)=-24/25
∵π/2≤α≤3π/4 ==>π≤2α≤3π/2
∴cos(2α)