题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040745-53299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040746-30923.png)
(1)求角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040746-32999.png)
(2)如果
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040746-73468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040746-24073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040746-59737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040747-29031.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040747-98930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040747-13764.png)
解析
试题分析:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040747-44872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040748-68713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040748-59907.png)
∴sin
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040747-44872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040748-59907.png)
∴原式可化为8cos2
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040748-59907.png)
∴4cos A+4-2(2cos2A-1)=7,
∴4cos2A-4cos A+1=0,解得cos A=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040748-35432.png)
(2)由余弦定理a2=b2+c2-2bccos A,
∴b2+c2-bc=3.
又∵b+c=3,∴b=3-c,
代入b2+c2-bc=3,并整理得c2-3c+2=0,
解之得c=1或c=2,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040747-98930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040747-13764.png)
点评:中档题,本题解答中,充分利用了函数方程思想,在求交点过程中往往求角的余弦,以避免增解。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040739-57095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040739-79817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040740-24758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040740-36986.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040740-24801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040740-95302.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040741-36137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040741-73891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040732-40069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040733-64704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040733-84434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040733-64277.png)
(Ⅰ)求角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040733-39475.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040734-16069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040734-73070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040734-26297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040729-30823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040729-77589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040729-66301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040723-31128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040723-52312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040723-27464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040723-83390.png)
(1)求角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040723-94902.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040723-31128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040723-31128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040710-63881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040710-29601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040710-63881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040710-84609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040710-15932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040710-63881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040711-71365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040711-32082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040711-81801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040711-96651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040711-86271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040711-54771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040711-43580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040711-57610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040712-13713.png)
(1)把
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040711-57610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040712-53225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040712-73679.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020040712-11386.png)
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