tan(α+

π

4

)＝2即

tanα+1

1−tanα

＝2
解得tanα＝

1

3

1+3sinα•cosα-2cos²α
=sin²α+3sinαcosα+cos²α
=

sin2α +3sinαcosα+cos2α

sin2α+cos2α

=

tan2α+3tanα+1

tan2α+1

=

1

10

故答案为

1

10