题目

已知向量a=（sinB，1-cosB）与向量b=（2，0）的夹角为，其中A、B、C是△ABC的内角. （1）求B的大小；（2）求sinA+sinC的取值范围. 答案：解：(1)∵A与B的夹角为， ∴=cos=.                                                                                              又∵===cos，                                                 且0＜＜,∴=,则B=.                                                                       (2)由(1)知,sinA+sinC=sinA+sin(-A)=sinA+cosA=sin(A+).                                                                                ∵0＜A＜,∴＜A+＜.∴sin(A+)∈(,1］,即sinA+sinC∈(,1］.

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