已知cot(a+拍/3)=-3则tan(2a-拍/3)=?

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已知cot(a+拍/3)=-3则tan(2a-拍/3)=?
已知cot(a+拍/3)=-3则tan(2a-拍/3)=?

已知cot(a+拍/3)=-3则tan(2a-拍/3)=?
cot(a+π/3)=-3=tan[π/2-(a+π/3)]=tan(π/6-a)=-tan(a-π/6)
tan(a-π/6)=3
tan(2a-π/3)=2tan(a-π/6)/[1-tan^2(a-π/6)]=6/(-8)=-3/4

已知cot(a+π/3)=-3则tan(2a-π/3)=?
tan(a+π/3)=-1/3
tan(2a+2π/3)=tan2(a+π/3)=2(-1/3)/[1-(-1/3)^2]=(-2/3)/(1-1/9)=-6/8=-3/4
tan(2a-π/3)=tan(-π+2a+2π/3)=tan(2a+2π/3)=-3/4