设三角形ABC的内角ABC的对边长分别为a,b,c,cos(A-C)+cosB=3/2，b^2=a

cos(A-C)+cosB =cos(A-C)-cos(A+C) =cosAcosC+sinAsinC-cosAcosC+sinAsinC =2sinAsinC =3/2 即sinAsinC=3/4 根据正弦定理， a/sinA=b/sinB=c/sinC=2R b^2=sin^B*4R^2 a=sinA*2R c=sinC*2R 所以，sin^B=sinA*sinC=3/4 因为B<180 所以，sinB=√3/