√3tanAtanB-tanA-tanB

解析：（1）√3*tanA*tanB-tanA-tanB=√3,也即是,tanA+tanB=-√3（1-tanA*tanB）故,tanC=-tan(A+B)=-（tanA+tanB)/(1-tanA*

1.倍角公式：cos2α=cos^2(α)-sin^2(α)=2cos^2(α)-1=1-2sin^2(α)3+cos4a-4cos2a=3+（2cos^2(2a)-1)-4(1-2sin^2(a))

√3×tanAtanB-tanA-tanB=√3∴tanA+tanB=-√3(1-tanAtanB)∴tan(A+B)=(tanA+tanB)/(1-tanAtanB)=-√3∴tanC=tan[π-

（1）tan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A+B)(1-tanAtanB)=tanA+tanB=根号3tanAtanB-根号3tan(A+B)=-根号3,tan(

tan(B+C)=(tanB+tanC)/(1-tanB*tanC)tanB+tanC+根号3tanBtanC=根号3,tanB+tanC=根号3-根号3tanBtanC=根号3*（1-tanB*ta

tanC=tan(180-(A+B))=-tan(A+B)=-(tanA+tanB)/(1-tanAtanB)tanA+tanB+3=3*tanAtanBtanA+tanB=3tanAtanB-3(t

由tanA+tanB+3=3tanAtanB可得tan（A+B）=tanA+tanB1-tanAtanB=-3因为A，B，C是三角形内角，所以A+B=120°，所以C=60°故答案为：60°

tanA+tanB=根号3*tanAtanB-根号3tanA+tanB=根号3(tanAtanB-1)tanA+tanB=-根号3(1-tanAtanB)(tanA+tanB)/(1-tanAtanB

（1）√3tanAtanB-tanA-tanB=√3√3tanAtanB-√3=tanA+tanB（tanA+tanB）/(1-tanAtanB)=-√3tan(A+B)=-√3∴A+B=120°∴C

tanA+tanB+√3=√3tanAtanBtanA+tanB＝√3(tanAtanB-1)所以-√3=(tanA+tanB)/[1-tanAtanB]tanC=tan(180-A-B)=-tan(

sinBcosB=（√3）/42sinBcosB=（√3）/2sin2B=（√3）/22B=60°,B=30°tanA+tanB=√3tanAtanB-√3,tanA+tanB=-√3(1-tanAt

由公式：tanA=a,tanB=b,tan（A+B）=（a+b）/(1-a*b)所以tan（A+B）=-√3,所以A+B=120度,所以角C=60度S△ABC=0.5*ab*sinc所以ab=6cos

1)根号3*tanAtanB-tanA-tanB=根号3tanA+tanB=根号3(tanAtanB-1)tan(A+B)=(tanA+tanB)/(1-tanAtanB)=根号3*(tanAtanB

不相等,正确的式子应该是tan(A+B)=tanA+tanB+tanAtanBtan(A+B)推倒的方式如下：∵tan(A+B)=(tanA+tanB)/(1-tanAtanB)tanA+tanB=(

1（√3）(tanAtanB+a)+2tanA+3tanB=0①(tanA+tanB)/(1-tanAtanB)=tan（A+B）=1/(√3）3(tanA+tanB)+(√3）（tanAtanB-1

tan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A+B)(1-tanAtanB)=tanA+tanB=根号3tanAtanB-根号3tan(A+B)=-根号3,tan(180

tanA+tanB+√3=√3tanAtanBtanA+tanB=-√3(1-tanAtanB)tan(A+B)=(tanA+tanB)/(1-tanAtanB0=-√3A+B=120,C=60度再由

∵tanA+tanB+√3tanAtanB=根号3∴等式两边同÷根号3,得（tanA+tanB）/根号3+tanAtanB=1移项得（tanA+tanB）/根号3=1-tanAtanB,∴tanAta

/>1.已知tanA+tanB=√3tanAtanB-√3,即(tanA+tanB)/(1-tanAtanB)=-√3tan（A+B）=(tanA+tanB)/(1-tanAtanB);所以tan（A

tanB+tanC+√3tanBtanC=√3可以化为：tanB+tanC=√3(1-tanBtanC)(tanB+tanC)/(1-tanBtanC)=√3即tan(B+C)=√3因为B,C都为三角