题目内容
(本小题满分13分)
设
的内角
的对边分别为
,且![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844424213.gif)
,
,求:
(Ⅰ)
的值;
(Ⅱ)
的值.
设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844361400.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844377291.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844408260.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844424213.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844439239.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844455243.gif)
(Ⅰ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844502224.gif)
(Ⅱ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844533368.gif)
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844549448.gif)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638445641371.gif)
解:(Ⅰ)由余弦定理得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844580567.gif)
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844595850.gif)
故
……6分
(Ⅱ)解法一:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844845359.gif)
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844876908.gif)
=
……9分
由正弦定理和(Ⅰ)的结论得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638449231577.gif)
故
……13分
解法二:由余弦定理及(Ⅰ)的结论有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638450481235.gif)
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163845063292.gif)
故![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638450791037.gif)
同理可得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638451101389.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638451261020.gif)
从而![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638451571378.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844580567.gif)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844595850.gif)
故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844549448.gif)
(Ⅱ)解法一:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844845359.gif)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844876908.gif)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163844892969.gif)
由正弦定理和(Ⅰ)的结论得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638449231577.gif)
故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163845032708.gif)
解法二:由余弦定理及(Ⅰ)的结论有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638450481235.gif)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823163845063292.gif)
故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638450791037.gif)
同理可得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638451101389.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638451261020.gif)
从而
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231638451571378.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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