tanα/(tanα-1)=-1
tanα=1-tanα
2tanα=1
tanα=1/2
sin²α+sinαcosα+2
=(1-cos2α)/2+1/2sin2α+2
=1/2-1/2*cos2α+1/2sin2α+2
=-1/2*cos2α+1/2sin2α+5/2
=-1/2*(1-tan²α)/(1+tan²α)+1/2*2tanα/(1+tan²α)+5/2
=-1/2*[1-(1/2)²]/[1+(1/2)²]+(1/2*2*1/2)/[1+(1/2)²]+5/2
=-1/2*[(3/4)]/[(5/4)]+(1/2)/(5/4)+5/2
=-1/2*3/5+2/5+5/2
=-3/10+4/10+25/10
=26/10
=13/5