△abc中,边8b=5c,角C=2B,求cosC
问题描述:
△abc中,边8b=5c,角C=2B,求cosC
答
正弦定理
b/sinB=c/sinC
b/c=sinB/sinC C=2B
5/8=sinB/2sinBcosB
10cosB=8 cosB=4/5
cosC=cos2B=2cos^2B-1=32/25-1=7/25