解题方法
1 . 某同学在一次研究性学习中发现,以下式子的值都等于同一个常数.①
;②
;③
;④
.
(1 )试从上述式子中选择一个,进行化简求值;
(2) 根据(1)的计算结果,将该同学的发现推广为三角恒等式,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb126b5ab256fc6e2acb7d13a0b8d037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7093e0b8e110dc530f1ef054b7a9dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b220c9c517d6ed89cc0ec4286970c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7d84540754ba1fbe20305c4ec53781.png)
(1 )试从上述式子中选择一个,进行化简求值;
(2) 根据(1)的计算结果,将该同学的发现推广为三角恒等式,并证明你的结论.
您最近一年使用:0次
2021-03-25更新
|
167次组卷
|
3卷引用:沪教版(2020) 必修第二册 同步跟踪练习 第6章 三角 6.2.1 第1课时 两角和与差的余弦
沪教版(2020) 必修第二册 同步跟踪练习 第6章 三角 6.2.1 第1课时 两角和与差的余弦沪教版(2020) 必修第二册 同步跟踪练习 第6章 6.2.1两角和与差的正弦、余弦、正切公式(已下线)专题22三角恒等变换-【倍速学习法】(人教A版2019必修第一册)
2 . 已知
为实数,
.
(1)若
,求关于
的方程
在
上的解;
(2)若
,求函数
,
的单调减区间;
(3)已知
为实数且
,若关于
的不等式
在
时恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77379b38d36d83e58fb18b4226f9a256.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9173b446b8ff3ec5506540f277d93a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9173b446b8ff3ec5506540f277d93a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a5dd65c213529071ee34a897ca009a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9c48e36f2c35dd8308029445332aa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-11-12更新
|
452次组卷
|
3卷引用:上海市控江中学2024届高三上学期期中数学试题
3 . 已知向量
,且
,常数
.
(1)若
,求函数
在
的严格增区间;
(2)设实数
满足
.若对任意
,不等式
都成立,求
的值以及方程
在闭区间
上的解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87caf889e87f095dbe8bbba6e5634dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7cb5138a03b19266f82223899a614f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcee772e6187ac31d7f8d69b0487000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4908e3b4e523c042732ccb7c215aac99.png)
(2)设实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b05662c741be8ecba731fde7d3fc7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb73539af255bde55d682b0d0ca735f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e4ba6d5f2eea68442def1911957fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
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解题方法
4 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ccb49239ecc5eb9062fd85aeddcce9.png)
(1)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b61e22083e790774ff7edec135a2a42.png)
(2)化简并求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ccb49239ecc5eb9062fd85aeddcce9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b61e22083e790774ff7edec135a2a42.png)
(2)化简并求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6f323b5287e5310a9e3e6a6f2a5cc7.png)
您最近一年使用:0次
名校
解题方法
5 . 设函数
的表达式为
,其中常数
.
(1)求函数
的值域;
(2)设实数
,
满足
,若对任意
,不等式
都成立,求
的值以及方程
在闭区间
上的解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e09f2bb67cb3920a4d54b8854ccf23e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)设实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1764838bed71962308a230961155f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70fa1faea71dd954ebb1dbaa822e282a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9e7131919449b3d2ebad852a1d78ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53496ae2397150370142b5195a1a39c.png)
您最近一年使用:0次
6 . 曾在北京召开的国际数学家大会会标如图,它是由4个相同的直角三角形与中间的小正方形拼成的一大正方形.已知大正方形的面积是1,小正方形的面积是
.记直角三角形中的一个锐角为
.
![](https://img.xkw.com/dksih/QBM/2021/3/22/2683279159386112/2685460832067584/STEM/114ca8b65fd64dfab72d395c4d89273f.png?resizew=145)
(1)根据本题题意写出
与
之间的等量关系,并求
的值;
(2)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf1ce0131607435c296520ad2558aac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/2021/3/22/2683279159386112/2685460832067584/STEM/114ca8b65fd64dfab72d395c4d89273f.png?resizew=145)
(1)根据本题题意写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1f30052674dba932701cbfa15195a3.png)
您最近一年使用:0次
名校
解题方法
7 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b196eb69a5777b46f00298c65acd93c1.png)
(1)化简
求值;
(2)若
,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b196eb69a5777b46f00298c65acd93c1.png)
(1)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b953f74e8a15470d39bb786230f67b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00079b8336c45a974223150c841af03c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa92f6b546937d3be81df143b5bd2ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eacde1c42151734fdc60f3001b590de.png)
您最近一年使用:0次
2023-08-01更新
|
969次组卷
|
4卷引用:上海市建平中学2024届高三上学期10月月考数学试题
上海市建平中学2024届高三上学期10月月考数学试题辽宁省沈阳市五校协作体2022-2023学年高一下学期期末联考数学试题(已下线)模块一 专题5三角恒等变换1(人教A版)期末终极研习室(已下线)高一上学期期末复习【第五章 三角函数】(拔尖篇)-举一反三系列
解题方法
8 . 已知
,且
.
(1)化简并求值:
;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f896ad30dbfae8a8fe6fc580a7af494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0f80c815f0ad841ffc0319ab1cd0f6.png)
(1)化简并求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9eeea7fdb06c25252eeea9e035211db.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59293d90383d56af29d8f8fd6d96af3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/336abb5d2a2a7f19f57a1dac867838ae.png)
您最近一年使用:0次
解题方法
9 . 设函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036719d5005ad21eca3e3e469c0148d9.png)
(1)讨论函数
的奇偶性,并说明理由;
(2)设
,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1cabea51106c6e9bc2f89f443c8542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036719d5005ad21eca3e3e469c0148d9.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e162d1739982517c1a337606c0e26573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a908ed89530a2f273684e5d014144d.png)
您最近一年使用:0次
名校
10 . 已知
且对任意
,不等式
无解,当实数
取得最大值时,方程
的解得个数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee6a07adbd93c4d2455c69e82bdf30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77af8a15bd425cee0fd4479371bbc538.png)
您最近一年使用:0次