题目内容
已知sin
+cos
=
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317107641511.png)
(1)求
的值 (2)求
的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710701310.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710701310.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710732500.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317107641511.png)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710779655.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710873720.png)
(I)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317109041004.png)
(II)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317109202694.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317109041004.png)
(II)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317109202694.png)
本试题主要是考查了二倍角公式和同角关系的运用。两角和的余弦公式的求解运算。
(1)根据已知条件,可知
,解得
,再根据又
,
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317111381028.png)
得到结论。
(2)因为
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231711294169.png)
于是![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317113411537.png)
结合两角和的公式得到结论。
解:(I)由题意得
,即
,
,
又
,
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317111381028.png)
(II)
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231711294169.png)
于是![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317113411537.png)
……8分
又![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317118712833.png)
(1)根据已知条件,可知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710935884.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710966670.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710998747.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231711029999.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317111381028.png)
得到结论。
(2)因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317112781134.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231711294169.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231711310904.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317113411537.png)
结合两角和的公式得到结论。
解:(I)由题意得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710935884.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231711481720.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710966670.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231710998747.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231711029999.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317111381028.png)
(II)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317112781134.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231711294169.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231711310904.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317113411537.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317118562684.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232317118712833.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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