题目内容
(本题满分12)
已知
,其中![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018612843.gif)
.若
图象中相邻的对称轴间的距离不小于
.
(1)求
的取值范围
(2)在
中,
分别为角
的对边.且
,当
最大时.求
面积.
已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018597482.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018612843.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018628855.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018643270.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018659233.gif)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018675201.gif)
(2)在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018690291.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018706260.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018721291.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018737648.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018675201.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018690291.gif)
(1) ![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018799849.jpg)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018815739.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018799849.jpg)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018815739.gif)
解:(1)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231500188311008.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018846671.gif)
……………………3分
由题意知![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018877589.gif)
……………………6分
(2)由于
1,由于(1)知
的最大值为1,
又![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018955665.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018971577.gif)
由余弦定理得
,又![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150019002272.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150019018421.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150019049277.gif)
……………………12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231500188311008.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018846671.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018862633.gif)
由题意知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018877589.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018893320.gif)
(2)由于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018909759.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018675201.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018940646.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018955665.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018971577.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018971408.gif)
由余弦定理得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018987351.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150019002272.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150019018421.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150019049277.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823150018815739.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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