名校
解题方法
1 . 如图,在正方体
中,点E,F分别是棱
,
的中点.
(1)求证:
平面
;
(2)求异面直线
与AF所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/27/48ce9f4e-f66e-4c29-a6ed-c42e509f560e.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4a94e889d2869ea84082575fae52ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d365ce9f4bacc4d4bb15dbdb5306a5.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
您最近一年使用:0次
2023-07-25更新
|
316次组卷
|
2卷引用:江西省萍乡市2022-2023学年高一下学期期末考试数学试题
解题方法
2 . 在
中,内角A,B,C所对的边分别为a,b,c,已知
.
(1)求B;
(2)若
,D为角B的平分线上一点,且
,求证:A,B,C,D四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68c4dddb95303d0a7987cc5579d5f05.png)
(1)求B;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098943e98ad321740f83f0bb67004598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
您最近一年使用:0次
解题方法
3 . 已知E,F分别为
的重心和外心,D是BC的中点,
,
.
(1)求BE;
(2)如图,P为平面ABC外一点,
平面ABC,二面角
的正切值为4.
①求证:
;
②求三棱锥
的外接球的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ace52b64e1e7dfc5211e033255b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13858be3c653034e71b88c205ac193d5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/28/499a650f-b18f-44cd-85ad-7ed2d0026b9e.png?resizew=180)
(1)求BE;
(2)如图,P为平面ABC外一点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90197a948331e61db644266368017e3.png)
②求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
名校
4 . 如图,在正方体
中,
分别为
的中点.
平面
;
(2)若正方体的棱长为4,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c644bd04a5e0d6ed487daa39bbcf4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad25d7eab7ecc7d46c19187adb9dc16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(2)若正方体的棱长为4,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef30620deef1165d60bd5d0dade9145.png)
您最近一年使用:0次
2023-08-22更新
|
421次组卷
|
3卷引用:云南省保山市腾冲市2022-2023学年高一下学期期中教育教学质量监测数学试题
云南省保山市腾冲市2022-2023学年高一下学期期中教育教学质量监测数学试题上海市松江二中2024届高三上学期阶段测试1数学试题(已下线)重难点专题14 利用传统方法解决二面角问题-【帮课堂】(苏教版2019必修第二册)
5 . 从条件①
,②
中选择一个,补充在下列横线中,并解答问题.
如图,在直三棱柱
中,点
在线段
上,已知______,且
,
,
.(若选择多个条件分别解答,则按第一个解答给分).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/3/416eee38-a3bc-4243-a403-b304040b9bb4.png?resizew=165)
(1)求证:
平面
;
(2)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429228f882da65a8e0064c88d02b8e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5181b97a7e43959b8455680157c3b644.png)
如图,在直三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9b8c14faadfc05738abbf67e1aa5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ad693aaa638917adbbbb947fadff75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68918379531894442f55c7257549ea33.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/3/416eee38-a3bc-4243-a403-b304040b9bb4.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231673dd67ab79d3c5da73904ceade1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
6 . 如图,在正三棱柱
中,
为
的中点,点
在
上,
,点
在直线
上,对于线段
上异于两端点的任一点
,恒有
平面
.
平面
;
(2)当
的面积取得最大值时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b9bcf4d4d165b5bfb9a272de9e34fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b5ee687274cd08dd8ac72b7e835022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36222db36e348661eb5f616820e4e60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c970a9c4f0da5435d02419d84de51d69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d4ceb3bf3b837d75225c04a96aa70d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e12d59170cdbf6ebfc754dd8f200bbd.png)
您最近一年使用:0次
2023-08-01更新
|
1321次组卷
|
7卷引用:宁夏吴忠市2022-2023学年高一下学期期末联合调研考试数学试题
宁夏吴忠市2022-2023学年高一下学期期末联合调研考试数学试题(已下线)第八章 立体几何初步(单元重点综合测试)-单元速记·巧练(人教A版2019必修第二册)(已下线)13.2.4 平面与平面的位置关系(2)-【帮课堂】(苏教版2019必修第二册)(已下线)专题02 高一下期末真题精选(2)-期末考点大串讲(人教A版2019必修第二册)(已下线)专题08立体几何期末14种常考题型归类(2) -期末真题分类汇编(人教B版2019必修第四册)(已下线)【一题多解】立体几何 新旧呼应(已下线)第二章 立体几何中的计算 专题一 空间角 微点10 二面角大小的计算综合训练【培优版】
解题方法
7 . 已知在
中,点M,N分别为AB,AC的中点.
(1)若
的面积为
,
,
,求
的长;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58d16c9d123c7c778f7abc3c8331242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b554899435e760da4791735db3338c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5555edf0bd4c08760dcc1d8fc54d11e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1973e77dbb01d8cf48b50e9b49499.png)
您最近一年使用:0次
解题方法
8 . 已知函数
的部分图象如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/7/38319f60-9b43-40aa-808f-23d9c3c3a3bb.png?resizew=152)
(1)求函数
的解析式;
(2)在
中,A为锐角且
,
,猜想
的形状并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f476b4c878b6ce23f5c392460f0d6d6c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/7/38319f60-9b43-40aa-808f-23d9c3c3a3bb.png?resizew=152)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a30cdeccc312028502c30ca324d62e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe29c42302504e7fd8577dbc7d130ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2023-08-06更新
|
507次组卷
|
3卷引用:海南省屯昌中学2022-2023学年高一下学期期中考试数学试题
名校
解题方法
9 . 在
中,内角A,B,C的对边分别为a,b,c,已知
.
(1)若
,求A;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536f9342cf73c2bcf1e7e79338fa1242.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759b29a7b2b3735306f1a650355a7858.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e73e25511809bdefbf2163dea1b6be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05d3b8f5c9df891ef6fbcaf12f43207.png)
您最近一年使用:0次
2023-11-27更新
|
1145次组卷
|
10卷引用:6.4.3.1余弦定理练习
6.4.3.1余弦定理练习山西省临汾市2023-2024学年高三上学期11月期中数学试题湖南省岳阳市湘阴县知源高级中学等多校2024届高三上学期11月月考数学试题(已下线)模块六 全真模拟篇 拔高1 期末终极研习室(2023-2024学年第一学期)高三(已下线)第04讲 正弦定理与余弦定理-【寒假预科讲义】(人教A版2019必修第一册)(已下线)专题04 平面向量的应用 (2)-【寒假自学课】(人教A版2019)(已下线)专题11 余弦定理-【寒假自学课】(苏教版2019)(已下线)6.4.3 课时1 余弦定理-高一数学同步精品课堂(人教A版2019必修第二册)(已下线)11.1 余弦定理-【帮课堂】(苏教版2019必修第二册)(已下线)专题11.1余弦定理-重难点突破及混淆易错规避(苏教版2019必修第二册)
名校
10 . 如图,在四棱锥
中,
,
,
,E是PA的中点,平面
平面ABCD.
(1)证明:
;
(2)证明:平面
平面PAC;
(3)求直线CE与平面PBC所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e19cb2532a1cc2c4368c587d2a4bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/7/bb13a1bf-92dd-47b4-bce4-a2f2017f2ec8.png?resizew=215)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
(3)求直线CE与平面PBC所成的角的正弦值.
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