1 . 请选择适当的方法证明下列结论:
(1)求证:
;
(2)已知
,求证:
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c1d583e670dac4530bd57ac9118740.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e10cc5dd849caccce37fe98a26c598.png)
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2022-04-02更新
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4卷引用:宁夏银川市贺兰县景博中学2022-2023学年高二上学期第二次月考数学(理)试题
21-22高三上·黑龙江哈尔滨·阶段练习
名校
2 . 如图,在直三棱柱
中,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98332901058e22626af97bff1b71039.png)
![](https://img.xkw.com/dksih/QBM/2021/2/19/2661504202792960/2661637481037824/STEM/62472c22-ab1a-4588-a0e1-7d5569c19892.png)
(1)证明:当
时,求证:
平面
;
(2)当
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/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98332901058e22626af97bff1b71039.png)
![](https://img.xkw.com/dksih/QBM/2021/2/19/2661504202792960/2661637481037824/STEM/62472c22-ab1a-4588-a0e1-7d5569c19892.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d06903252260d31d1a9cdeb735b089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8845fadc307f1d308410e829becedd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ceb31247add8ca7b0853e801e1d125.png)
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解题方法
3 . 如图所示
,
,侧面
底面
若
.
![](https://img.xkw.com/dksih/QBM/2021/1/5/2629475259146240/2632465580244992/STEM/6c14c863-eed0-4976-908e-903062322c2d.png?resizew=249)
(1)求证:
平面PAC;
(2)侧棱PA上是否存在点E,使得
平面PCD?若存在,指出点E的位置并证明,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef699f5dc072b853cfe700c6f1abbbae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1141247167a3d1584ae774f3fb164321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebbb79892c8cb8871a08437acc09bc80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702f9d7ff83e48e10187bd66b45beecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af3d91d89c75231ba82c9cf6aff92a6.png)
![](https://img.xkw.com/dksih/QBM/2021/1/5/2629475259146240/2632465580244992/STEM/6c14c863-eed0-4976-908e-903062322c2d.png?resizew=249)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28fa14d4841ca3f2fe226688c25c8160.png)
(2)侧棱PA上是否存在点E,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5258a6f9c63914b9e2ec95b6d39313b2.png)
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2021-01-09更新
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4卷引用:宁夏固原市第五中学2023-2024学年高二上学期9月月考数学试题
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4 . 用反证法证明“设
,求证
”时,第一步的假设是______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127a0d8c1c7d15ed40ec4b8bca0ebdf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485a2d99320384a0857b00ce9ab9e990.png)
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2020-03-20更新
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7卷引用:宁夏六盘山高级中学2019—2020学年高二下学期第一次月考测数学试题
5 . (1)求证
.
(2)设x,y都是正数,且x+y>2证明:
和
中至少有一个成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ffe492bb9af2b14bac592bbc72cd3d.png)
(2)设x,y都是正数,且x+y>2证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe6efd706e0d6fd5921c8ba41866c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994a46413196d5150c865507aea411ae.png)
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9卷引用:【全国百强校】宁夏回族自治区平罗中学2018-2019学年高二下学期期中考试数学(文)试题
【全国百强校】宁夏回族自治区平罗中学2018-2019学年高二下学期期中考试数学(文)试题河南省周口市郸城县实验高中2019-2020学年高二下学期第二次月考数学(理)试题河南省新乡市辉县市第二高级中学2019-2020学年高二下学期期中考试数学(理)试题河南省新乡市辉县市第二高级中学2019-2020学年高二下学期期中考试数学(文)试题安徽省安庆市第十中学2020-2021学年高二下学期第一次月考文科数学试题安徽省芜湖市第一中学2020-2021学年高二下学期期中理科数学试题山西省晋中市新一双语学校2020-2021学年高二下学期3月月考数学(理)试题河南省新乡市河南师大附中实验学校2021-2022学年高二下学期期中考试数学文科试题2019届陕西省宝鸡市宝鸡中学高三上学期10月第一次模拟考试数学(文)试题(A卷)
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6 . 已知△
中,
,求证
.
证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7efa75e1f580910d41d954bc911cd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0caa3e6a0de075df4c9a869dfed4bf20.png)
画线部分是演绎推理的( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c0ad68bf0ca0d00461a269df127af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7efa75e1f580910d41d954bc911cd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0caa3e6a0de075df4c9a869dfed4bf20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf1aa83a61bd003e09b68d51af984a4.png)
A.大前提 | B.三段论 | C.结论 | D.小前提 |
您最近一年使用:0次
2017-07-15更新
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3卷引用:宁夏石嘴山市第三中学2017-2018学年高二上学期期末考试数学(文)试题
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7 . 选择适当的方法证明.
已知:
,求证:
.
已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9185519a1b1928d6cd4147f43c738145.png)
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2017-03-08更新
|
496次组卷
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2卷引用:宁夏海原第一中学2020-2021学年高二下学期第二次月考数学(文)试题
8 . 在长方体
中,
,过
、
、
三点的平面截去长方体的一个角后,得到如图所示的几何体
,
、
分别为
、
的中点.
平面
;
(2)求平面
与平面
的夹角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066b3dc118e127eaeee4005bfec77134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52eab6de89f4d4e69650e94e0968744.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/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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解题方法
9 . 如图,在直三棱柱
中,
,
,
,
分别为棱
,
,
的中点,
,
.
(1)求证:平面
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/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc416a5b8dc234628e7475387888d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baa1c07becd03537beeb09a31745cf5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/24/ccb57f24-3146-4b9c-bb74-4fe3e822edf5.png?resizew=140)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f592e3002c6973654b154812ed360c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ad564d8ee60c950612b78f42f5ecb0.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212a67f115d1cbe69f100b489babe5f8.png)
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2023-11-23更新
|
929次组卷
|
2卷引用:宁夏青铜峡市宁朔中学2023-2024学年高二上学期第二次月考数学试题
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10 . 如图,在四棱锥
中,
平面
,
.
,E为
的中点,点
在
上,且
.
(1)求证:
平面
;
(2)求二面角
的正弦值;
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d73337f55b68fe4c10e77a9c4212811b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8eb7be08ab924bd4e6360633e4ab383.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88454ace46996b99361d18e76189cdc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/7/e0ff9114-5363-4a63-ad79-7b827f192a80.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74011b64ff147ac2f10c36a11ac1b34d.png)
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2024-01-22更新
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