Question

设△ABC的三个内角A、B、C，向量m＝(sinA，sinB)，n＝(cosB，cosA)，若m·n＝1＋cos(A＋B)，则C＝(　　)

A.                                                              B.

C.                                                             D.

Answer 1

C

[解析]　m·n＝sinAcosB＋sinBcosA＝sin(A＋B)＝sinC，cos(A＋B)＝－cosC，∵m·n＝1＋cos(A＋B)，∴sinC＝1－cosC，∴sin(C＋)＝，

∵0<C<π，∴C＝.