1 . 已知实数
满足:①
;②存在实数
,使得
,
,
是等差数列,
,
,
也是等差数列.则实数
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e633d15ed77937c15180d0593fabde03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7931c14dc4e055e3d0b709b9c080b6df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68a9723a0e94b16a6019a2494f103f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fc27f36003850ea40fb1d9cf18d462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebea760067502e24ddf3d1e541be36ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
2 . 已知
为椭圆:
(
)上一点,
,
为左、右焦点,设
,
,若
,则该椭圆的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e49877a18188a806e5bc312264796bf.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](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/280d2a6b2a0d45904635f528319fc635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f1ea4a7412e643e4b47263e434f2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3267f5af8b2f64309db15a2eb1afc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e49877a18188a806e5bc312264796bf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/ffb78fce-cf8b-4c06-a6ab-95864f9f4377.png?resizew=172)
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2024-01-10更新
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1310次组卷
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5卷引用:江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(九)
江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(九)湖南省长沙市第一中学2024届高三上学期月考数学试卷(五)湖南省大联考长沙市一中2024届高三上学期月考数学试卷(五)(已下线)考点12 三角恒等变换公式的综合应用 --2024届高考数学考点总动员【讲】江西省宜春市丰城市第九中学2023-2024学年高一上学期期末数学试题
3 . 求值:
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e1fdd5c8f2c66909cbdfd10880d243.png)
A.![]() | B.![]() | C.1 | D.![]() |
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2023-11-02更新
|
2508次组卷
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6卷引用:湖南省2024届高三数学新改革适应性训练二(九省联考题型)
湖南省2024届高三数学新改革适应性训练二(九省联考题型)江苏省苏州市梁丰高级中学2023-2024学年高三上学期10月模拟数学试题(已下线)第四章 三角函数与解三角形 专题 12 三角恒等变换中的求值问题 高中数学优质试题一题多解和变式训练(已下线)专题05 三角函数4-2024年高一数学寒假作业单元合订本(已下线)【公式证明】和差公式 口诀处置(已下线)8.2.4 三角恒等变换的应用-【帮课堂】(人教B版2019必修第三册)
4 . 设
是定义域为
的函数,如果对任意的
、
均成立, 则称
是“平缓函数”.
(1)若
, 试判断
和
是否为“平缓函数” ? 并说明理由; (参考公式:
时,
恒成立)
(2)若函数
是“平缓函数”, 且
是以 1为周期的周期函数, 证明:对任意的
、
, 均有
;
(3)设
为定义在
上函数, 且存在正常数
使得函数
为“平缓函数”. 现定义数列
满足:
, 试证明:对任意的正整数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1076aeb555debc8bf15c586375d64c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2fe919afe3583b1ef0dadbd23102a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70458945dae62f8f6a553dfaa8eb723a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b40b099989abb2d15ddf60413c8a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640461197eaf70c0ebe1eb89daf383c1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33890c6b0bf167514d44139d9dca0154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49a2b43fdce5aaae58c0907de23cbc6c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6bf90a1bbeea09e1b7206975a99f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66efdaa9fe939b2b1a7326aaf5e35d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f422484ad3a17eeebc4d15a3fb6289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848ea90ecbd6c506a78058f983ff5614.png)
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解题方法
5 . 在
中,
对应的边分别为
,且
.且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c9b04e29a3334fd8f6156e6e1f8aa1.png)
(1)求
;
(2)若
,
上有一动点
(异于B、C),将
沿AP折起使BP与CP夹角为
,求
与平面
所成角正弦值的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271edf347d9890c3b4838fa35fc2b298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c9b04e29a3334fd8f6156e6e1f8aa1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668c8ab5abdba7173bcbe573ae87dad4.png)
![](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/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
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解题方法
6 . 已知单位向量
满足
,
,则对任意
,
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6033601ebf591c1c3b7a95dd00bbb81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56ce68a9988c3eab2c652abdc89b89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf60e507d2a72cf010998c7bc494754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c95134ef4808453772f5354fc08275.png)
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2022-01-26更新
|
1080次组卷
|
4卷引用:浙江省四校2022届高三下学期联考数学试题
浙江省四校2022届高三下学期联考数学试题浙江省金华十校2021-2022学年高三上学期期末联考数学试题(已下线)专题4-1 三角函数性质、最值和w小题归类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)上海市进才中学2024届高三上学期开学考试数学试题
名校
7 . 已知函数
,现给出如下结论:①
是奇函数;②
是周期函数;③
在区间
上有三个零点;④
的最大值为
.其中所有正确结论的编号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308e0fc6877f72f5a7f14eafaeea01bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfe8e7fb253685e0e50bae0c5482314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
A.①③ | B.②③ | C.②④ | D.①④ |
您最近一年使用:0次
2021-05-14更新
|
1912次组卷
|
5卷引用:陕西省西安交通大学附属中学2021届高三下学期第四次模拟考试理科数学试题
陕西省西安交通大学附属中学2021届高三下学期第四次模拟考试理科数学试题(已下线)考点突破05 三角函数-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)(已下线)第五章 三角函数(选拔卷)-【单元测试】2021-2022学年高一数学尖子生选拔卷(人教A版2019必修第一册)山东省淄博市美达菲双语高级中学2022-2023学年高一下学期3月月考数学试题(已下线)专题14 三角函数的图象与性质压轴题-【常考压轴题】
8 . 已知
是定义在
上的函数,如果存在常数
,对区间
的任意划分:
,和式
恒成立,则称
为
上的“绝对差有界函数”。注:
。
(1)证明函数
在
上是“绝对差有界函数”。
(2)证明函数
不是
上的“绝对差有界函数”。
(3)记集合
存在常数
,对任意的
,有
成立
,证明集合
中的任意函数
为“绝对差有界函数”,并判断
是否在集合
中,如果在,请证明并求
的最小值;如果不在,请说明理由。
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804319e6cb58f07ee82ee364e334f36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7bba359204c3a83c5094e9bc09e4f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2955a1ae6ca7b3a7c9fd5b3e7bdc09.png)
(1)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587882ac081850caa4447c44a7dbb845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4b97703638756a4051a3dd0cdcf5a6.png)
(2)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf20df06f5ff3e00e38f3e257f2ea6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2130dde27163d8ae5a28aae9467e24b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f20b947d584a1dc48676c2ae6e2af52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9bc59028761bee9de313ee6d5decc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ba29e6b864f89b4772130b6dc87427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa611cda56d55165309bdfbbf58240c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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