Question

在三角形ABC中,角A,B,C对应的边分别为a,b,c已知8b=5c,C=2B则cosC=

Answer 1

8b=5c
8sinB=5sinC
sinC=sin2B=2sinBcosB
8sinB=10sinBcosB
cosB=4/5
sinB=3/5
sinC=2sinBcosB=2*4/5*3/5=24/25
cosC=7/25

Answer 2

正弦定理：b/sinB=c/sinC得5/8c*sinC=c*sibB得5/8sinC=sinB得5/8sin2B=sinB得5/8*2sinBcosB
两边消去sinB的cosB=4/5即cosC/2=4/5
由二倍角公式cosC=2cos^2(C/2)-1得cosC=7/25