求值:4sin20°+tan20°=_.

问题描述:

求值:4sin20°+tan20°=______.

4sin20°+tan20°=4sin20°+

sin20°
cos20°
=
sin20°+4sin20°cos20°
cos20°

=
(sin20°+sin40°)+sin40°
cos20°
=
2sin30°cos10°+sin40°
cos20°

=
cos10°+cos50°
cos20°
=
2cos30°cos20°
cos20°
=
3

故答案为:
3