1 . 若定义在
上的函数
满足对任意实数
恒成立,则我们称
为“类余弦型”函数.
(1)已知
为“类余弦型”函数,且
,求
和
的值;
(2)在(1)的条件下,定义
,求
的值;
(3)若
为“类余弦型”函数,且对任意非零实数
,总有
,求证:函数
为偶函数.设有理数
满足
,判断
和
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc57d42b2adbff8dfa18f45a5eb69703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8492210fbc3ea3678bbc96c6b35240e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
(2)在(1)的条件下,定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8eb899087bfa2bf4a9a58105f72c849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207d8709a7dc0f5e85b64b8f0a1ab504.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caea9a696f22c76f8f4563ac45d124b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c983d456ac12b40aea1fd87e961c07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9769116ec47353514e6b7fb7b17216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542893790445d6d888d9ff91fd215c9c.png)
您最近一年使用:0次
2 . (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)
您最近一年使用:0次
2019-06-25更新
|
893次组卷
|
9卷引用: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
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【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)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
3 . 如图,在三棱柱ABC−
中,
平面ABC,D,E,F,G分别为
,AC,
,
的中点,AB=BC=
,AC=
=2.
(2)求二面角B−CD−C1的余弦值;
(3)证明:直线FG与平面BCD相交.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
(2)求二面角B−CD−C1的余弦值;
(3)证明:直线FG与平面BCD相交.
您最近一年使用:0次
2018-06-09更新
|
14797次组卷
|
34卷引用:【全国百强校】山西省祁县中学2018-2019学年高二上学期期末模拟一考试数学(理)试题
【全国百强校】山西省祁县中学2018-2019学年高二上学期期末模拟一考试数学(理)试题2018年全国普通高等学校招生统一考试理科数学(北京卷)(已下线)2018年高考题及模拟题汇编 【理科】5.立体几何【全国百强校】江西省南昌市第十中学2017-2018学年高二下学期期末考试数学(理)试题北京市2019届高三数学理一轮复习典型题专项训练:立体几何四川省棠湖中学2018-2019学年高二上学期期末考试数学(理)试题(已下线)专题8.6 空间向量及空间位置关系(练)【理】-《2020年高考一轮复习讲练测》(已下线)专题8.6 空间向量及空间位置关系(讲)【理】-《2020年高考一轮复习讲练测》江苏省徐州市侯集高级中学2019-2020学年高二上学期期末数学试题2020届北京市昌平区新学道临川学校高三上学期第三次月考数学(理)试题2020届北京市昌平区新学道临川学校高三上学期第三次月考数学(文)试题(已下线)专题06 立体几何(解答题)——三年(2018-2020)高考真题理科数学分项汇编(已下线)专题17 立体几何综合-五年(2016-2020)高考数学(理)真题分项山西省山西大学附中2019-2020学年高二(12月份)第四次诊断数学(理科)试题(已下线)专题8.6 空间向量及其运算和空间位置关系(精讲)--2021年高考数学(理)一轮复习讲练测(已下线)专题8.6 空间向量及其运算和空间位置关系(精讲)-2021年高考数学(理)一轮复习学与练(已下线)专题4.4 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)四川省成都市双流区棠湖中学2018-2019学年高二上学期期末数学(理)试题云南省昭通市昭阳第一中学2020-2021学年高一12月月考数学(理)试题北京市第四十三中学2020-2021学年高二下学期第一次月考数学试题(已下线)专题10 立体几何-五年(2017-2021)高考数学真题分项(新高考地区专用)(已下线)第37讲 立体几何中的向量方法 (讲) — 2022年高考数学一轮复习讲练测(课标全国版)福建省泉州科技中学2021-2022学年高二上学期第一次月考数学试题北京市昌平区第一中学2021-2022学年高二上学期期中考试数学试题北京市景山学校2021-2022学年高二上学期期中考试数学试题辽宁省沈阳市五校协作体2021-2022学年高二上学期期中数学试题北京市第九中学2022届高三12月统练(月考)数学试题(已下线)专题8.7 立体几何中的向量方法(练)【理】-《2020年高考一轮复习讲练测》(已下线)专题24 空间向量与空间角的计算-十年(2011-2020)高考真题数学分项(已下线)重组卷03北京外国语大学附属中学2022届高三模拟数学试题北京十年真题专题07立体几何与空间向量北京市第一零一中学2023-2024学年高三上学期数学统练五云南省大理白族自治州民族中学2023-2024学年高二下学期5月期中数学试题
名校
4 . 用综合法或分析法证明:
(1)如果
,则
;
(2)求证:
.
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7c5b6f00c87aeb530c599206ec3c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67906845ad74da01d00e5c6f160a0077.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f0bd054e7efc73bb10431d5f1020aa.png)
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5 . 如图,四棱锥
的底面是正方形,侧棱
⊥底面
是
的中点.
(Ⅰ)求证:
∥
;
(Ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f449e8cd3075c1de5cae3a57293f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6d94889ef44776a1a60586922ee891.png)
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509d8dd6031dc0ef92075877e53fe201.png)
![](https://img.xkw.com/dksih/QBM/2017/11/15/1817625011290112/1819374978760704/STEM/dc9e51a78fac47e59bc20c1aae79dcbe.png?resizew=166)
您最近一年使用:0次
2017-11-17更新
|
936次组卷
|
5卷引用:山西省晋中市祁县第二中学校2019-2020学年高二上学期期中数学试题
6 . 如图所示,几何体
中,
为正三角形,
⊥
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/a15545170482467ca8259ae9b6a02d2a.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/f5c84d2c77754645981cf009655bdd3e.png)
(Ⅰ)在线段
上找一点
,使
平面
,并证明;
(Ⅱ)求证:面![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/f4e858865c104d9798ec8910a7d427e0.png)
面
.
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/7f34ac7ee01c4107b6f54d254b51d4ed.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/35b306f6a62948428a4b93bddbf4db0d.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/40a0ad6f22a24c49a7a46bf96f74aad2.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/fc52f295e9fe4290a28875c7775b221b.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/6a3efad2c7eb4ba0a7429b984738d51e.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/ca16472278ac43038181035a2bcbbfbf.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/a15545170482467ca8259ae9b6a02d2a.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/f5c84d2c77754645981cf009655bdd3e.png)
(Ⅰ)在线段
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/9ec406f7e44a4dafbedc329c8714f48e.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/460973d273ec46f4b73d39735df27bd4.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/b83f5735f3204a0cb211ad52e80bbffb.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/29074dad5f1f4cbc9dadc5d2bf742f10.png)
(Ⅱ)求证:面
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/f4e858865c104d9798ec8910a7d427e0.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/621ec4a94c3043f583ba7bcdf14f1c72.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496357728256/1572496363315200/STEM/8956364b1ef94f13a2d90e94c4b05d8a.png)
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7 . 已知函数
,其中
为自然对数的底数.
(1)若
对任意的
恒成立,求实数
的取值范围;
(2)设
的导数为
,若
,求证:关于
的方程
在区间
上有实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731136e5167c920ba9d7afa6647fa378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58a948b004e915762b76525e142aed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdad8acb5f4d31bfee990bf844b1a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d069a6d759c880149329bb9c477e038b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
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8 . 如图,在三棱锥
中,底面
是等腰直角三角形,
,
,且
,
为
的中点.
平面
;
(2)若二面角
的大小为
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc223bc59d4c5b1c99f811e4bded9783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc83f34b5a3c1dc09d990ce4bdc8e078.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6d1c5eace748465b2dad5065f5111c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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解题方法
9 . 如图,在六面体
中,
,
,且
,
平行于平面
,
平行于平面
,
.
平面
;
(2)若点
到直线
的距离为
,
为棱
的中点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93efb8cd8d8b27301c3b15c8493721fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4519397ce1e517777092f9037e73aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e19e9ca6a8de8831644937765fb23b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4611ceb2a28f7a7e4d24266d7f99b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
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解题方法
10 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
的右焦点为
,直线
与
交于
,
两点,
(1)若
过点
,点
,
到直线
的距离分别为
,
,且
,求
的方程;
(2)若点
的坐标为
,直线
过点
交
于另一点
,当直线
与
的斜率之和为2时,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43fbcf7a16e2dcf66b22c81989d0471d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/de72a5190834f5dbe895596656c038b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356904bae80ce41c871e2a905058fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b1ba4307cfde9b424d468bfcdf6c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe9a0dc4298b1f283d0f728a231a375.png)
您最近一年使用:0次