解题方法
1 . 阅读:序数属性是自然数的基本属性之一,它反映了记数的顺序性,回答了“第几个”的问题.在教材中有如下顺序公理:①如果
,那么
;②如果
,那么
.
(1)请运用上述公理①②证明:“如果
,那么
.”
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe96cc58c73271a157f908b4261620a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069390dd908ff203327958117a226593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dac0a497d02926a23678d5dc6bcf79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34c5832f3fe28f48a924854cb8814ba.png)
(1)请运用上述公理①②证明:“如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6c4658978e20d4074a1099de1e15a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f50ce6b511e6b928796e048fc7fa5c.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af26bd7fd83da5267ed64b3f22ad59a0.png)
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名校
2 .
(1)苏教版《普通中学教科书数学必修第一册》第70页第16题可得出以下基本不等式:当
,
时,
(当且仅当
时,等号成立).试用上述结论证明:当
时,
;
(2)如图,锐角
(单位为弧度)的终边与单位圆交于点
,作
轴于点
.
![](https://img.xkw.com/dksih/QBM/2022/4/11/2955971972710400/2957941185773568/STEM/fda1db2c-afa0-4d09-9fa7-934c2a8acdf0.png?resizew=212)
(i)利用单位圆与三角函数线证明:当
时,
;
(ii)求
的周长与面积之和的取值范围.
(1)苏教版《普通中学教科书数学必修第一册》第70页第16题可得出以下基本不等式:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b603108c964254b841b9058ffd60ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6eec7d75a66a4407631f75320bb8b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae3371f6c2f0038a239e47a6d72a435.png)
(2)如图,锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3a3db6d96518255f96ad7fc1ac98f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2022/4/11/2955971972710400/2957941185773568/STEM/fda1db2c-afa0-4d09-9fa7-934c2a8acdf0.png?resizew=212)
(i)利用单位圆与三角函数线证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6eec7d75a66a4407631f75320bb8b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba65bdcf4f2f04f800a496618888f6e.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56b0348213284a19e2acc5a088fa491.png)
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20-21高一·江苏·课后作业
3 . 证明:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6e89ff670f9a10eb087a02051f3a50.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c573bd16158492f3c6533261d2188b.png)
您最近一年使用:0次