因为

1+tanx

1−tanx

=2 010，
则

1

cos2x

+tan2x=

1

cos2x

+

sin2x

cos2x

=

1+sin2x

cos2x

=

(sinx+cosx)2

cos2x−sin2x

=

cosx+sinx

cosx−sinx

=

1+tanx

1−tanx

=2010．
故答案为：2010