2sin20°+cos10°+tan20°sin10°
=2sin20°+cos10°+

sin20°sin10°

cos20°

=

2sin20°cos20°+cos10°cos20°+sin20°cos10°

cos20°

=

sin40°+cos10°

cos20°

=

cos50°+cos10°

cos20°

=

2cos30°•cos20°

cos20°

=2cos30°
=

3

．
故答案为：

3

．