△ABC的三个内角A、B、C所对的边分别为a,b,c,asinAsinB+bcos2A=2a,则ba=(  ) A.23 B.22 C.3 D.2

问题描述:

△ABC的三个内角A、B、C所对的边分别为a,b,c,asinAsinB+bcos2A=

2
a,则
b
a
=(  )
A. 2
3

B. 2
2

C.
3

D.
2

∵asin AsinB+bcos2A=

2
a
∴由正弦定理可知sin2AsinB+sinBcos2A=
2
sinA
∴sinB(sin2A+cos2A)=sinB=
2
sinA
sinB
sinA
=
b
a
=
2

选D