∵tanα=1/3
∴sinα/cosα=1/3
∴cosα=3sinα
sin^2α+sinαcosα+2cos^2α
=(sin^2α+sinαcosα+2cos^2α)/(sin²α+cos²α)
=(sin²α+3sin²α+2*9sin²α)/(sin²α+9sin²α)
=22sin²α/(10sin²α)
=11/5
∵tanα=1/3
∴sinα/cosα=1/3
∴cosα=3sinα
sin^2α+sinαcosα+2cos^2α
=(sin^2α+sinαcosα+2cos^2α)/(sin²α+cos²α)
=(sin²α+3sin²α+2*9sin²α)/(sin²α+9sin²α)
=22sin²α/(10sin²α)
=11/5