Question

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

Answer 1

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