三角形ABC中,边abc成等比数列,CosB=3/4.1.求(1/tanA)+(1/tanC)的值.2.设向量BA*BC=3/2,求a+c

abc成等比数列 b^2=ac,
(sinB)^2=sinAsinC
(1/tanA)+(1/tanC)=sosA/sinA+cosC/sinC
=(cosAsinC+cosCsinA)/sinAsinC
=sin(A+C)/sinAsinB
=sinB/sinAsinC=1/sinB=4根号7/7向量BA*BC=accosB=3ac/4=3/2
ac=2 cosB=(a^2+c^2-b^2)/2ac
3/4=((a+c)^2-2ac-ac)/2ac
3/4=(a+c)^2-6)/4 a+c= 3