解题方法
1 . 如图1,在梯形
中,
,
,
.将
与
分别绕
,
旋转,使得点
,
相交于一点,设为点
,形成图2,且二面角
与二面角
都是45°.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/96e5eed3-fe94-428c-8e3b-abd7b4640074.png?resizew=340)
(1)证明:平面
平面
;
(2)若
,且梯形
的面积为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4611ceb2a28f7a7e4d24266d7f99b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ff7bf8ffc8a04186e3e13c1a6d5ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d437e27d4b6251b07f46798526b6999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc917beae4ae9df9707bc82b35cd629.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/96e5eed3-fe94-428c-8e3b-abd7b4640074.png?resizew=340)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f020ca4ad44801691235958e253907d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0589d1fb13c06ff2f5d1cd58bfa206.png)
您最近一年使用:0次
2021-03-06更新
|
1332次组卷
|
3卷引用:广东省揭阳市2021届高三下学期教学质量测试数学试题
广东省揭阳市2021届高三下学期教学质量测试数学试题(已下线)专题08 空间向量在立体几何中的应用-备战2021年高考数学二轮复习题型专练(新高考专用)广东省佛山市南海区南海艺术高级中学2022届高三下学期第四次综合测试数学试题
解题方法
2 . 已知
,
分别为椭圆
的左、右焦点,
为
的上顶点,
,且
的面积等于1.
(1)求
的方程;
(2)若过点
的直线
交
于另外一点
,
关于直线
对称的直线为
,
交
于另外一点
(异于点
),证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288060bacca802a86ff209ddfd412e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2021-03-05更新
|
318次组卷
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3卷引用:广东省揭阳市普宁市普师高级中学2021届高三下学期二模数学试题
3 . 如图,在三棱锥
中,
,D在底面
上的射影E在
上,
于F.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/5b505c3c-08aa-4625-9f28-a59053f204a3.png?resizew=185)
(1)求证:
平行平面
,平面
平面
;
(2)若
,求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0f630195bcf6c3ca8f4fdeff43b082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa30a9ee227af2b387cf6e028c20d7d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/5b505c3c-08aa-4625-9f28-a59053f204a3.png?resizew=185)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905e950cc8fc6f92f31c62c784cbbc26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca86d6c18154a268342269171d7f1d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aad963ee7cdc7ff35a8dd23685589d1.png)
您最近一年使用:0次
2021-03-04更新
|
730次组卷
|
2卷引用:广东省揭阳市普宁市华侨中学2021届高三下学期二模数学试题
名校
4 . 下列说法正确的是( )
A.已知椭圆以坐标轴为对称轴,且长轴长是短轴长的![]() ![]() ![]() |
B.等轴双曲线![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.平面内到点![]() ![]() ![]() |
D.设![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2021-02-25更新
|
585次组卷
|
2卷引用:广东省普宁市2020-2021学年高二上学期期末数学试题
解题方法
5 . 已知:如图所示的几何体中,正方形
所在平面垂直于平面
,四边形
为平行四边形,
为
上一点,且
平面
,
.
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649630773452800/2653421974921216/STEM/3bd6dee4d116472288465b34fe15aa68.png?resizew=151)
(1)求证:平面
平面
;
(2)当
时,求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf65b8884909d735d575efe81a2d2ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649630773452800/2653421974921216/STEM/3bd6dee4d116472288465b34fe15aa68.png?resizew=151)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6760f565c694d1cdb6d7068e14526d00.png)
您最近一年使用:0次
解题方法
6 . 设
、
为椭圆
的左、右顶点,若在椭圆上存在异于
、
的点
,使得
,其中
为坐标原点,则椭圆的离心率
的取值范围是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e137562b63a5452f1d6401d2115f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
您最近一年使用:0次
解题方法
7 . 正三棱柱(底面是正三角形的直棱柱)
的底面边长为
,侧棱长为
,则
与
所成的角为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
您最近一年使用:0次
名校
8 . 已知集合
,
或
.
(1)当
时,求
;
(2)当
时,若“
”是“
”的充分条件,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8c6d32c0077bf7e075af3e4150c09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585742f70872c634b889f852e23e845f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cf5ab959efb5b142e21ccfb3182964.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021-02-05更新
|
3849次组卷
|
14卷引用:广东省普宁市第二中学2021-2022学年高一上学期第一次月考数学试题
广东省普宁市第二中学2021-2022学年高一上学期第一次月考数学试题福建省泉州市2020-2021学年高一上学期期末数学试题江苏省苏州市新区苏州实验中学2020-2021学年高一下学期期初数学试题(已下线)2.3二次函数与一元二次方程、不等式(专题强化卷)-2021-2022学年高一数学课堂精选(人教版A版2019必修第一册)(已下线)试卷08(第1章-3.2 基本不等式)-2021-2022学年高一数学易错题、精典题滚动训练(苏教版2019必修第一册)(已下线)第1章 集合与常用逻辑用语 章末测试(基础)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第一册)(已下线)第2章 常用逻辑用语 单元综合检测(单元培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)(已下线)第2章 常用逻辑用语(强化篇)-2021-2022学年高一数学单元过关卷(苏教版2019必修第一册)(已下线)2.2 充分条件、必要条件、充要条件-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)江苏省泰州市兴化市昭阳中学2022-2023学年高一上学期第一次月度检测数学试题河南省开封市通许县启智高中2022-2023学年高一上学期第一次月考数学试题青海省西宁北外附属新华联外国语高级中学2022-2023学年高一上学期期中考试数学试题湖南省湘西州吉首市2022-2023学年高二上学期基础教育综合实践改革成果展示活动检测数学试题 福建省泉州市泉州中远学校2023-2024学年高一上学期第一阶段教学质量检测数学试题
名校
解题方法
9 . 如图,在直三棱柱
中,
,
,
分别为侧棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649456150011904/2651679379013632/STEM/967c2f61abe948b0997626223e235fdc.png?resizew=113)
(1)证明:
平面
;
(2)求
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/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af30873743bc357559cc6bd8b5241c26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649456150011904/2651679379013632/STEM/967c2f61abe948b0997626223e235fdc.png?resizew=113)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d365ce9f4bacc4d4bb15dbdb5306a5.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d365ce9f4bacc4d4bb15dbdb5306a5.png)
您最近一年使用:0次
2021-02-05更新
|
397次组卷
|
5卷引用:广东省普宁市第二中学2020-2021学年高二下学期第一次月考数学试题
解题方法
10 . 已知圆
与
轴的交点为
、
,以
、
为左、右焦点的双曲线
的右支与圆
交于
、
两点,若直线
与
轴的交点恰为线段
的一个四等分点,则双曲线的离心率等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7121bfdb53eb8307706e8c63c4569b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-02-04更新
|
1094次组卷
|
4卷引用:广东省普宁市华美实验学校2021届高三下学期二模数学试题