1/tanA+1/tanB = cosA/sinA+cosB/sinB = (cosAsinB+cosBsinA)/sinAsinB=sin(A+B)/sinAsinB
因为C=120 ,所以A+B=60 ,sin(A+B)=3^0.5/2 ; 2sinAsinB = cos(A-B)-cos(A+B)= cos(A-B)-1/2
原式= 3^0.5/(cos(A-B)-1/2) ,所以原式在cos(A-B)=1 ,即A-B=0时,最小 为 2*3^0.5