tan23°+tan37°+3tan23°tan37°= _ .
问题描述:
tan23°+tan37°+
tan23°tan37°= ___ .
3
答
∵23°+37°=60°,tan60°=
3
∴tan(23°+37°)=
=tan23°+tan37° 1-tan23°•tan37°
,
3
去分母整理,得tan23°+tan37°=
-
3
tan23°tan37°,
3
∴原式=
-
3
tan23°tan37°+
3
tan23°tan37°=
3
.
3
故答案为:
3