△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=
a,则
2
=( )b a
A. 2
3
B. 2
2
C.
3
D.
2
答
∵asin AsinB+bcos2A=
a
2
∴由正弦定理可知sin2AsinB+sinBcos2A=
sinA
2
∴sinB(sin2A+cos2A)=sinB=
sinA
2
∴
=sinB sinA
=b a
2
选D