解答题-证明题 适中0.64 引用3 组卷437
在如图所示的空间几何体中,平面
平面
,
与
是边长为
的等边三角形,
,
和平面
所成的角为
,且点
在平面
上的射影落在
的平分线上.
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/983a7bbd82d246258d820d2cf6155367.png)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/3b46f3c75aa847a3940791f0f6578f0d.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/7ab0623173af482695cf318b90a0ea83.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/09070f2461fc48b192826660ad167cbd.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/5ec8756f1a9a4d19a7d72270b0c4be54.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/a6e1671439f64fbf9bef202e2ab9a471.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/9a9413c6fa264733b3518928509a5b0c.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/a6a0081bf66e40b1a399df82b29e2ab6.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/7ab0623173af482695cf318b90a0ea83.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/1d9d8b5244864ee3a89faac301b22602.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/e49aebcd926b492f93f9b64adc526b0d.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/7ab0623173af482695cf318b90a0ea83.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/a8282077fd614507905a5ddee3fc60ce.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/983a7bbd82d246258d820d2cf6155367.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/52815a849f81458e83e0f709d49d7fc2.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/7ab0623173af482695cf318b90a0ea83.png)
(2)求二面角
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572507975041024/1572507981225984/STEM/687d85108a63415482fac84ee2699e4d.png)
15-16高三上·山西·期中
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