2014高三·全国·专题练习
名校
解题方法
1 . 如图所示,
是棱长为
的正方体,
、
分别是棱
、
上的动点,且
.当
、
、
、
共面时,平面
与平面
所成锐二面角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f8eebda19eded2b059774a8c2666c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431e8bf1a5f9ac9a2ec82c11f31a4afe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/30/2f73d0ed-b712-4311-b7e7-908efe8145fd.png?resizew=146)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-11-26更新
|
1156次组卷
|
22卷引用:甘肃省天水市、平凉市2022届高三一模数学(理)试题
甘肃省天水市、平凉市2022届高三一模数学(理)试题甘肃省陇南、临夏、甘南三地2022-2023学年高三上学期期中联考理科数学试题甘肃省兰州市等3地2022-2023学年高二上学期期中数学试题甘肃省平凉市2023届高三上学期期中数学(文科)试题甘肃省兰州市等2地、天水市第三中学等2校2022-2023学年高二上学期期中数学试题(已下线)2015届高考数学(理)一轮总复习专题突破四 高考立体几何2018秋人教A版高中数学选修2-1第三章测评人教A版(2019) 选择性必修第一册 必杀技 第一章 空间向量与立体几何 1.4 空间向量的应用 1.4.2 用空间向量研究距离、夹角问题 课时2 用空间向量研究夹角问题人教B版(2019) 选择性必修第一册 必杀技 第一章 空间向量与立体几何 1.2 空间向量在立体几何中的应用 1.2.4 二面角山东省济宁市曲阜市第一中学2020-2021学年高二阶段性检测(9月月考)数学试题(已下线)专题44 空间向量及其应用(同步练习)-2021年高考一轮数学(理)单元复习一遍过天津市武清区杨村第三中学2020-2021学年高二(上)第一次月考数学试题(已下线)专题44 空间向量及其应用(同步练习)-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题07 立体几何中的向量方法-备战2021届高考数学(理)二轮复习题型专练?(通用版)北师大版(2019) 选修第一册 必杀技 第三章 4.3 课时1 用空间向量研究夹角问题(已下线)专练7 用空间向量研究距离、夹角问题-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)(已下线)专练12 空间向量与立体几何综合检测卷(B卷)-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)黑龙江省七台河市勃利县高级中学2021-2022学年高二上学期期中考试数学试题2023版 北师大版(2019) 选修第一册 突围者 第三章 全章综合检测第三章空间向量与立体几何单元测试 2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册(已下线)艺体生一轮复习 第七章 立体几何 第36讲 空间向量在立体几何中的应用【讲】(已下线)艺体生一轮复习 第七章 立体几何 第35讲 空间向量及其运算【练】
名校
2 . 如图,三棱柱
的侧面
是边长为
的正方形,面
面
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2020/11/19/2596487620116480/2597812554776576/STEM/93053e4164f64515b27e7e22ad96e37a.png?resizew=298)
(1)求证:
平面
;
(2)求点
到平面
的距离;
(3)在线段
上是否存在一点
,使二面角
为
,若存在,求
的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6480f384476190883f06c0289c7519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ca47585273d02911e4eb87f01c8354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d498a0467ff3c577a7ed175d7bffd885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650a59e187c0f9b854293bf316422a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/2020/11/19/2596487620116480/2597812554776576/STEM/93053e4164f64515b27e7e22ad96e37a.png?resizew=298)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b46a7e819a5ed0b789f1f06bb0076422.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b46a7e819a5ed0b789f1f06bb0076422.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbbf91d6bac18e969cbb0015a16c9e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
您最近一年使用:0次
2020-11-21更新
|
688次组卷
|
2卷引用:甘肃省平凉市庄浪县第一中学2021届高三上学期第四次模拟数学(理)试题
解题方法
3 . 已知直四棱柱
的所有棱长相等,
,则直线
与平面
所成角的正切值等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d4e574c9d139615d991a168cfbf63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
4 . 如图,四棱锥
的底面为直角梯形,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/60d58999-c216-4baf-9096-fa981dad0909.png?resizew=214)
(Ⅰ)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(Ⅱ)若平面
平面
,异面直线
与
所成角为60°,且
是钝角三角形,求二面角
的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e45b6f8cf0260912f587c04f9f2442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf7ee20cc8113e5685dca7ba6f9adeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/60d58999-c216-4baf-9096-fa981dad0909.png?resizew=214)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f369bec2d5682bf6b8b317a08aff546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(Ⅱ)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
2020-09-02更新
|
371次组卷
|
7卷引用:甘肃省武威第六中学2020届高三下学期第六次诊断考试数学(理)试题
甘肃省武威第六中学2020届高三下学期第六次诊断考试数学(理)试题2020届山东省济宁市高三5月(二模)模拟数学试题天津市第七中学2022届高三下学期线上第一次阶段检测数学试题(已下线)第33讲 空间中的平行关系-2021年新高考数学一轮专题复习(新高考专版)(已下线)专题1.4空间向量的应用-2020-2021学年高二数学同步课堂帮帮帮(人教A版2019选择性必修第一册)陕西省西安工业大学附属中学2022届高三下学期第七次模拟考试理科数学试题陕西省西安工业大学附属中学2022届高三下学期第七次适应性训练理科数学试题
名校
解题方法
5 . 如图①,在菱形
中,
且
,
为
的中点,将
沿
折起使
,得到如图②所示的四棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/3d120806-7143-43c1-813e-ad31c1ab32c8.png?resizew=340)
(1)求证:平面
平面
;
(2)若
为
的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/3d120806-7143-43c1-813e-ad31c1ab32c8.png?resizew=340)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7ba7cd0c654714c967a900513ba16.png)
您最近一年使用:0次
2020-08-14更新
|
1637次组卷
|
12卷引用:甘肃省天水市第一中学2021届高三十模数学(理)试题
甘肃省天水市第一中学2021届高三十模数学(理)试题四川省成都市2021届高三毕业班摸底测试数学理科试题安徽省合肥市第八中学2021届高三下学期高考模拟最后一卷理科数学试题四川省武胜烈面中学校2020-2021学年高三9月月考数学(理)试题重庆复旦中学2020-2021学年高二下学期期中数学试题福建省上杭一中、永定一中2022届高三上学期第一次联考数学试题广东省深圳市福田区外国语高级中学2022届高三上学期第二次调研考试数学试题湖南省长沙市长郡中学2021-2022学年高三上学期月考(三)数学试题湖北省黄石市有色一中2021-2022学年高二上学期10月月考数学试题湖北省鄂州市鄂城区秋林高级中学2022-2023学年高二上学期10月月考数学试题江苏省淮安市盱眙中学2021-2022学年高三上学期期中数学试题重庆市永川北山中学校2023届高三下学期入学考试数学试题
名校
6 . 如图,四棱锥
的底面为等腰梯形,
,
,
,侧面
为正三角形,
![](https://img.xkw.com/dksih/QBM/2020/7/20/2510138099916800/2511476433543168/STEM/b7fa2791-5182-49c4-a06d-da1d087e295e.png)
(1)求证:
平面
;
(2)在线段
上存在一点
,满足
,求
值使得平面
与平面
和平面
所成二面角相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21158c6a4bb5d42e75fef98bf72ca27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a895c63ec5b8f15565df016f5b3f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de3001f5075daddcc8d817ac95b6c70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74456e2b1dbde29393f8c07527047209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50244defdb202cc420e1d6a910241c8.png)
![](https://img.xkw.com/dksih/QBM/2020/7/20/2510138099916800/2511476433543168/STEM/b7fa2791-5182-49c4-a06d-da1d087e295e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7767d492158189b23af332a8016ed37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df915a088300b53c298fecd10675e5b.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeab094d8cdd70e3352b9b32b14e84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558ce69401f3c97930f00ba0e2aa6647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89abfe070487c1296d855093aa9596e4.png)
您最近一年使用:0次
2020-07-22更新
|
245次组卷
|
2卷引用:甘肃省静宁县第一中学2020届高三第四次模拟考试数学(理)试题
名校
7 . 如图,四边形
为正方形,
平面
,
,点
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/7/20/2510137895624704/2511274969260032/STEM/f053eb30-3751-4128-9454-cefc83e924cb.png)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d4d36ae30487030b827ce9413b9f13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2682f3f3f0f72c893b99073bcac83ff2.png)
![](https://img.xkw.com/dksih/QBM/2020/7/20/2510137895624704/2511274969260032/STEM/f053eb30-3751-4128-9454-cefc83e924cb.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
您最近一年使用:0次
2020-07-22更新
|
266次组卷
|
2卷引用:甘肃省靖远县2020届高三仿真高考冲刺理科数学试题
名校
解题方法
8 . 如下图所示,四棱锥
中,
底面
,
,
为
的中点,底面四边形
满足
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/3a55247c-ae02-4c77-8a83-648aea9d3c64.png?resizew=161)
(Ⅰ)求证:平面
平面
;
(Ⅱ)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9a31b4fce9307e48458fa5ce44779c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70c0e9d65544456c8767f851a658088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/3a55247c-ae02-4c77-8a83-648aea9d3c64.png?resizew=161)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac48b9ac8efbf41d6ab5242d247bd89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a49de08c6527101927582945d6551bf.png)
您最近一年使用:0次
名校
9 . 如图,已知三棱柱
中,平面
平面ABC,
,
.
![](https://img.xkw.com/dksih/QBM/2020/7/9/2502377418481664/2504067813048320/STEM/87d920da95854bd1a8341b8cc0f194ce.png?resizew=178)
(1)证明:
;
(2)设
,
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fe926770d2354e172dec02f5ce2efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://img.xkw.com/dksih/QBM/2020/7/9/2502377418481664/2504067813048320/STEM/87d920da95854bd1a8341b8cc0f194ce.png?resizew=178)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47af45fbf1714055d9b414a44a8613fa.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8c563906d6d25078fd5d96abe96194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e718d2042232538370f5168f7eb9a1.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,三棱锥
中,
,A、D分别为
、
的中点,
,
,平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/af55e85b-d761-4190-b242-56d09d00b896.png?resizew=153)
(1)证明:
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84160ab4c7e760ae3a09d1cce623a49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef95ebb3e3e81f72c609203f0a046a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e04cc7a52c3ad292d937bfa4507343e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d502002ad65d8bc45f71693fb79256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f464948420e7b666335bfd60f7678e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/af55e85b-d761-4190-b242-56d09d00b896.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71b7cbc7958bc5a520aad74842e59e8.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3336e307c79e059770bf1a46d2974df7.png)
您最近一年使用:0次