题目内容
(本小题满分12分)
已知函数
.
(1)设
,且
,求![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403712292.png)
的值;
(2)在△ABC中,AB=1,
,且△ABC面积为
,求sinA+sinB的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403603158.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232034036191302.png)
(1)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403665667.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403697613.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403712292.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403806164.png)
(2)在△ABC中,AB=1,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403821628.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403853425.png)
解(1)
=
=
.
由
,得
,
于是
,因为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404024161.png)
,所以
.
(2)因为
,由(1)知
.
因为△ABC的面积为
,所以
,于是
. ①
在△ABC中,设内角A、B的对边分别是a,b.
由余弦定理得
,所以
. ②
由
①②可得
或
于是
.
由正弦定理得
,所以
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232034038841189.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403899782.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403931977.png)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232034039461110.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403977916.png)
于是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232034039931009.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404024161.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404071660.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404102675.png)
(2)因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404118569.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404149511.png)
因为△ABC的面积为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203403853425.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404227920.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404289542.png)
在△ABC中,设内角A、B的对边分别是a,b.
由余弦定理得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232034043211049.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404383510.png)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404492164.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404523740.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404539747.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404555584.png)
由正弦定理得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823203404570970.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232034045861144.png)
略
![](http://thumb.zyjl.cn/images/loading.gif)
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