已知数列{an}为等差数列,且a1+a7+a13=π,则tan(a2+a12)的值为(  ) A.3 B.−3 C.±3 D.−33

问题描述:

已知数列{an}为等差数列,且a1+a7+a13=π,则tan(a2+a12)的值为(  )
A.

3

B.
3

C. ±
3

D.
3
3

∵数列{an}为等差数列,∴a1+a13=a2+a12=2a7
∵a1+a7+a13=π,∴3a7=π,解得a7

π
3

则tan(a2+a12)=tan(2a7)=tan
3
=-tan
π
3
=−
3

故选B.