2021·全国·模拟预测
名校
解题方法
1 . 如图,在正三棱柱
中,点D为棱BC的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882961348149248/2883220302872576/STEM/3dc04c019e1844bbbc2adbbf8d34141e.png?resizew=207)
(1)证明:
;
(2)若点E为棱AB上一点,且满足______,求二面角
的正弦值.
从①
;②
这两个条件中任选一个填入上面的横线上,并解答问题.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882961348149248/2883220302872576/STEM/3dc04c019e1844bbbc2adbbf8d34141e.png?resizew=207)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06769ce64b9bc0a23ead087fc7f8c55e.png)
(2)若点E为棱AB上一点,且满足______,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c07c2e932d60994bd58a04dd193f39.png)
从①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176a1127a464fed085df602e1e235c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d382176514c5da39e93a8e15cf4e2f74.png)
注:如果选择多个条件分别解答,按第一个解答计分.
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