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解题方法
1 . 设n次多项式
,若其满足
,则称这些多项式
为切比雪夫多项式.例如:由
可得切比雪夫多项式
,由
可得切比雪夫多项式
.
(1)若切比雪夫多项式
,求实数a,b,c,d的值;
(2)已知函数
在
上有3个不同的零点,分别记为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27a496e3bd84636a630b74ff7eb8587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a324d249a3bd683015e6fb6883bc4af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb54c94f215d294a68aae1111c4f83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9eb1248ec39be5efeefa829db095928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fdfb3b6462b724510577f3f11ca6ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91d0d02d04a3f1b777b0d86e2372e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941da3ce63a15fecbb77e4d8ade8fcf7.png)
(1)若切比雪夫多项式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07821e71f17322d3b3555d07bceb8d8.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daaf6fb508f82d4e9d50a708ae2d9814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2c5f7b63a7dd6d0155f9d38158fcf1.png)
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2023-06-20更新
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462次组卷
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2卷引用:湖北省襄阳市第四中学2023-2024学年高一下学期质量检测(一)数学试题
2 . 已知
为锐角三角形,且
.
(1)证明:
;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ddce89498b5d0f74d11fbcae2563eb.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09eebab59213386449a726b75065bf76.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17145b1c12c95ae02e401a8db98c6f51.png)
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2022-09-14更新
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3卷引用:湖北省荆州市公安县第三中学2022-2023学年高三上学期9月月考数学试题
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3 . 观察以下等式:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b0f45966c30d12d5772424b61980f.png)
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dc0fcf260db515d8128c44be89bac9.png)
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031bec2b4a8d027a2388e4d8fd04d3a9.png)
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ae99de91b3f23bd0e828c54a96b926.png)
⑤![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cab538c99ba4d0ca62a489926fd951c.png)
(1)对①②③进行化简求值,并猜想出④⑤式子的值;
(2)根据上述各式的共同特点,写出一条能反映一般规律的等式,并对等式的正确性作出证明.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b0f45966c30d12d5772424b61980f.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dc0fcf260db515d8128c44be89bac9.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031bec2b4a8d027a2388e4d8fd04d3a9.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ae99de91b3f23bd0e828c54a96b926.png)
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cab538c99ba4d0ca62a489926fd951c.png)
(1)对①②③进行化简求值,并猜想出④⑤式子的值;
(2)根据上述各式的共同特点,写出一条能反映一般规律的等式,并对等式的正确性作出证明.
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2022-02-17更新
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7卷引用:湖北省武汉市新高考联合体2021-2022学年高一下学期期末数学试题
湖北省武汉市新高考联合体2021-2022学年高一下学期期末数学试题广东省茂名市电白区2021-2022学年高一上学期期末数学试题广东省佛山市顺德区华侨中学2021-2022学年高一下学期3月月考数学试题(已下线)模块三 专题7 大题分类练(三角恒等变换)拔高能力练(北师大版)(已下线)模块三 专题5 大题分类练(三角恒等变换)拔高能力练(苏教版)福建省福州市日升中学2023-2024学年高一上学期12月月考数学试题广西百色市平果市铝城中学2023-2024学年高一上学期期末数学解答题专项训练(二)
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4 . 已知在
中,
为钝角,
,
.
(1)求证:
;
(2)设
,求
边上的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c293d258052c478c62a063831bdf3d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639d5d9508f2ff5e976b03270f2e19bd.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff09908d8a83f8349d062dc2503c5d49.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2020-12-11更新
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4卷引用:湖北省十一校考试联盟2020-2021学年高三上学期12月联考数学试题
5 . 若在定义域内存在实数x0,使得f(x0+1)=f(x0)+f(1)成立,则称函数f(x)是“可拆函数”.
(1)函数f(x)=
是否是“可拆函数”?请说明理由;
(2)若函数f(x)=2x+b+2x是“可拆函数”,求实数b的取值范围:
(3)证明:f(x)=cosx是“可拆函数”.
(1)函数f(x)=
![](https://img.xkw.com/dksih/QBM/2016/2/25/1572499453583360/1572499459522560/STEM/2b98da9ab1674108b9188baac9049193.png)
(2)若函数f(x)=2x+b+2x是“可拆函数”,求实数b的取值范围:
(3)证明:f(x)=cosx是“可拆函数”.
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