Question

若tan(

π

4

-θ)=3，则

cos2θ

1+sin2θ

=______．

Answer 1

∵tan（

π

4

-θ）=

1-tanθ

1+tanθ

=3，
∴tanθ=-

1

2

，
则

cos2θ

1+sin2θ

=

cos2θ-sin2θ

sin2θ+cos2θ+2sinθcosθ

=

1-tan2θ

tan2θ+1+2tanθ

=

1- 1 4

1 4 +1-1

=3．
故答案为：3