解题方法
1 . 在四棱锥
中,
,
,
和
都是边长为2的等边三角形,设
在底面
的射影为
.
![](https://img.xkw.com/dksih/QBM/2017/3/6/1637836956491776/1637877409349632/STEM/1dacb0c3dca44570a0eed6935e086711.png?resizew=182)
(1)求证:
是
中点;
(2)证明:
;
(3)求点
到面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72db7e94c6f876ca3ff61613a4d92d9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cb9d85db1c73459d93b0abf927718c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2017/3/6/1637836956491776/1637877409349632/STEM/1dacb0c3dca44570a0eed6935e086711.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da48240e7fc3248f773ac1500c15ec14.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2017-03-06更新
|
1577次组卷
|
2卷引用:2017届广西柳州市、钦州市高三第一次模拟考试数学(文)试卷
名校
2 . 在四棱锥
中,
,
,
和
都是边长为2的等边三角形,设
在底面
的射影为
.
![](https://img.xkw.com/dksih/QBM/2017/3/6/1637836815663104/1637860221419520/STEM/9f3f9bef-f847-4992-9bc4-4e514e3a462c.png?resizew=184)
(1)求证:
是
中点;
(2)证明:
;
(3)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db08db31046bf98eb01abfbf356059ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c235aa3c3d273fdf205b1057eea7439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2017/3/6/1637836815663104/1637860221419520/STEM/9f3f9bef-f847-4992-9bc4-4e514e3a462c.png?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da48240e7fc3248f773ac1500c15ec14.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
您最近一年使用:0次
2017-03-06更新
|
883次组卷
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5卷引用:2017届广西柳州市、钦州市高三第一次模拟考试数学(理)试卷
3 . 已知椭圆
的左、右顶点分别为
,长轴长为4,离心率为
,点C在椭圆E上且异于
两点,
分别为直线
上的点.
(1)求椭圆E的方程;
(2)求
的值;
(3)设直线
与椭圆E的另一个交点为D,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fb2098ccf6cfb30a679960969ce400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
(1)求椭圆E的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbfb05e2ec0eb61fde5339fa2809ad7.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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4 . 如图,在四棱锥
中,四边形ABCD为正方形,
平面ABCD,
,F是PB中点,
平面PBC;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced3d3dd6af84fb052fc7281d707853e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a22d6b860f06fe23618b0d3de6768fa.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907ff109ed2739140db28bc4b2617bf7.png)
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名校
解题方法
5 . 如图,在直三棱柱
中,
,点
是棱
上的一点,且
,点
是棱
的中点.
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37daee5542600d83c05b45cbe0750bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c05e654d3ee1ca86bc42cd20ca302c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cfdc6224181d44e63aab43ddaf07ef.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2024-03-21更新
|
1548次组卷
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6卷引用:广西柳州高级中学2024届高三下学期5月适应性演练数学试卷
6 . 如图所示,在直四棱柱
中,底面ABCD是菱形,
,M,N分别为
,AD的中点.
平面BDM.
(2)求平面BDM与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1634a7ca88281066e1a8db2f9008c2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f845e74c18cdb2d6a80e0c0b4e85cd.png)
(2)求平面BDM与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6931032c7feb343c8d423a0d456d2f.png)
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名校
7 . 如图(1),在
中,
,
,
,
分别是
,
的中点,将
和
分别沿着
,
翻折,形成三棱锥
,
是
中点,如图(2).
(1)求证:
平面
;
(2)若直线
上存在一点
,使得
与平面
所成角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e7d395bc97771671c5001a52138313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09a769a75b107390b9eeccc929f761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212b200cb65843fe03aab377d53991d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/c9c51067-307b-48e7-a4df-d5298c2b636d.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7442b64b37f685bc3ae88ff450c1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3d566704b44ea4ef1f99c37bd46902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785f4eb0787ffc744fb1018f0c6c347f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
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2024-02-04更新
|
242次组卷
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2卷引用:广西柳州市柳州高级中学2023-2024学年高二上学期开学考试数学试卷
解题方法
8 . 已知奇函数
(
)
(1)求实数
的值;
(2)判断并用定义证明函数
的单调性;
(3)若函数
在区间
(
)上的取值范围为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b6ffbd30cce0d2ffe6fd360abf7d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断并用定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7a69be4f38695f6fe58b4e3268549e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
9 . 如图,在四棱锥
中,底面
是边长为4的正方形,
平面
.点
在侧棱
上(端点除外),平面
交
于点
.
为直角梯形;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84db6d8c048fa2387cc4c63a3df72753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18952f3e04d465e8b654619e9978053b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
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2024-05-12更新
|
441次组卷
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3卷引用:广西柳州铁一中学2023-2024学年下学期高一五月月考数学试题
名校
解题方法
10 . 在
中,角A,B,C所对的边分别为a,b,c,且
.
(1)证明:
为等腰三角形.
(2)若D是边BC的中点,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2818bff73d7e297bfbcda3d22d1a153.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若D是边BC的中点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9af00d442a5c693c970f30efcc916f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-06-11更新
|
1262次组卷
|
3卷引用:广西柳州市第一中学2023-2024学年高二下学期阶段性期中考试数学试题