Question

在△ABC中,sin(A+B)=4/5,cosB=-2/3,cosA=

A.-3/5 B.4√5-6/15 C.6-4√5/15 D.6+4√5/15
求详细解析过程！谢谢

Answer 1

选D

Answer 2

∵cosb=-2/3
∴90<b<180, sinb=√ 5/3
∵sin(a+b)=4/5
∴90<a+b<180,cos(a+b)=-3/5
cosa =cos[(a+b)-b]=cos(a+b)cosb+sin(a+b)sinb =2/5+4√ 5/15=(6+4√ 5)/15