cotA+cotC=cosA/sinA+cosC/sinC
=(cosAsinC+cosCsinA)/sinAsinC
=sin(A+C)/sinAsinC
=sinB/sinAsinC
根据正弦定理.a/sinA=b/sinB=c/sinC=k.
所以a=ksinA,b=ksinB,c=ksinC.
因为a,b,c成等比数列,所以k^2sinB^2=k^2sinAsinC推出sinAsinC=sinB^2
所以sinB/sinAsinC=1/sinB,因为cosB=3/4,所以sinB=(7^(1/2))/4.
所以原式等于：七分之四倍根号七.