tan23°+tan37°+3tan23°tan37°= _ .

问题描述:

tan23°+tan37°+

3
tan23°tan37°= ___ .

∵23°+37°=60°,tan60°=

3

∴tan(23°+37°)=
tan23°+tan37°
1-tan23°•tan37°
=
3

去分母整理,得tan23°+tan37°=
3
-
3
tan23°tan37°,
∴原式=
3
-
3
tan23°tan37°+
3
tan23°tan37°=
3

故答案为:
3