题目内容
设A、B、C是△ABC的三个内角,且sin2B + sin2C = sin2A +
sinBsinC,则2sinBcosC – sin (B – C)的值为( )
A.
B.
C.
D.![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150608349205.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150608287209.gif)
A.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150608302245.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150608318241.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150608334249.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150608349205.gif)
D
由sin2B + sin2C = sin2A +
sinBsinC可得sinA =![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150608349205.gif)
而2sinBcosC– sin (B – C) =" sin" (B + C) = sinA.故选D.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150608287209.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150608349205.gif)
而2sinBcosC– sin (B – C) =" sin" (B + C) = sinA.故选D.
![](http://thumb.zyjl.cn/images/loading.gif)
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