名校
解题方法
1 . 如图所示,在四棱锥
中,
是等边三角形,
,
,记平面ACD与平面ABE的交线为l.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/0ebd465e-0fc2-4d92-bd2f-4988226b2541.png?resizew=158)
(1)证明:
.
(2)若
,
,Q为l上一点,求BC与平面QBD所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2550fca125b1f9e31f65701e4d0637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9c7cbcc38b28d45c8539710e5b260a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/0ebd465e-0fc2-4d92-bd2f-4988226b2541.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56adc934c9ad3cb261c5cbdc346b9631.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef62a37b18982ace39a6c8fa4157112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cd134aa49a8c75736772e1381f6b5cf.png)
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2023-02-02更新
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3卷引用:山西省吕梁名师高级中学校2022-2023学年高二下学期开学考试数学试题