tan10°+tan50°+3tan10°tan50°的值为(  ) A.-3 B.3 C.3 D.33

问题描述:

tan10°+tan50°+

3
tan10°tan50°的值为(  )
A. -
3

B.
3

C. 3
D.
3
3

tan10°+tan50°+

3
tan10°tan50°
=tan(10°+50°)(1-tan10°tan50°)+
3
tan10°tan50°
=
3
(1-tan10°tan50°)+
3
tan10°tan50°
=
3
-
3
tan10°tan50°+
3
tan10°tan50°
=
3

故选:B.