tan（-25派/12）等于多少?
问题描述：
tan（-25派/12）等于多少?
答
tan（-25派/12）
=tan(-2派-派/12)
=-tan(派/12)
=√3-2
答
tan(π/6)=tan(π/12+π/12)=2tan(π/12)/(1-tan²π/12)=√3/3
2tanπ/12=√3/3-√3/3tan²π/12
(√3/3)tan²(π/12)+2tan(π/12)-√3/3=0
得
tan(π/12)=[-2±√(4+4/3)]/2√3/3
=-√3±2
因为 tanπ/12>0
所以 tanπ/12=-√3+2
tan(-25π/12)=tan(-2π-π/12)=tan(-π/12)=-tan(π/12)=√3-2
答
tan(－25π/12)=－tan(25π/12)=－tan(π/12)
因为tan(a/2)=sina/(1＋cosa),则tan(π/12)=sin(π/6)/[1＋cos(π/6)]=(1/2)/[1＋(√3/2)]=2－√3
则：tan(－25π/12)=√3－2