问题
填空题
已知△ABC中,内角A,B,C所对的边分别为a,b,c,若a,b,c成等比数列,且cosB=
|
答案
因为cosB=
>0,所以sinB=3 4
=1-cos2B
,7 4
由a,b,c成等比数列得到b2=ac,根据正弦定理得:
=a sinA
=b sinB
,c sinC
而cotA+cotC=
+cosA sinA
=cosC sinC
=sin(A+C) sinAsinC sin(π-B) sinAsinC
=
=sinB sinAsinC
•sin2B sinAsinC
=1 sinB
•sinB sinA
•sinB sinC
=1 sinB
•b a
•b c
=1 sinB
=1 sinB
=1 7 4 4 7 7
故答案为:4 7 7