解题方法
1 . 在
中,角
的对边分别为
,
,
.
(1)判断
的形状,并给出证明;
(2)若
,点D在边
上,且
的周长为
,求
的周长.
![](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/f289ef19c7418a898ea18747aa76e783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8266e004b9ef28e94e564d771f602e2f.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de861ddb3aaa93d449d319f9c3ea11f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
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2 . 在
中,角
所对的边分别是
,且
.
(1)证明:
成等比数列.
(2)求(1)中数列的公比的取值范围和角
的最大值.
![](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/ccd2268e2cc4579245fdfd9e91cff600.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4a8c2c7845cfb1b094d13e66e0ed87.png)
(2)求(1)中数列的公比的取值范围和角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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3 . 在锐角
中,角
的对边分别为
为
的面积,且
.
(1)求
的值;
(2)若
,证明:
.
![](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/84d8b760e8712cca692c729c0f83842b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c28d53e229fcea80c26b22d9e1a94ac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aae1dc870a60a2070469d556deb472.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e15cbd7c42d7b15d7ba8d2b28ab8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880d5fb6a76f76f48d841590c9f79743.png)
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4 . 如图,
中,点
为边
上一点,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/b29777a0-4a5c-4750-89ef-074576da0804.png?resizew=182)
(1)证明:
;
(2)若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7702345faab336ee91d6be0360be8cef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/b29777a0-4a5c-4750-89ef-074576da0804.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10082dfd9158a2bb317d0dc6939ae0c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1493dbac7cd1e48196056a0d5c1529e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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3卷引用:甘肃省张掖市某重点校2022-2023学年高三上学期11月月考数学(文)试题
甘肃省张掖市某重点校2022-2023学年高三上学期11月月考数学(文)试题河南省安阳市2022-2023学年高三上学期一轮复习联考(二)全国卷文科数学试题(已下线)广东省汕头市2023届高三第一次模拟数学试题变式题17-22
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解题方法
5 . 如图,△ABC中,点D为边BC上一点,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/c1ea66fe-1e1e-4864-99a2-185c66373637.png?resizew=214)
(1)证明:
;
(2)若AB=2,AC=1,
,求△ABD的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7702345faab336ee91d6be0360be8cef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/c1ea66fe-1e1e-4864-99a2-185c66373637.png?resizew=214)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de47573a39d8540ed1ae433628fcdca0.png)
(2)若AB=2,AC=1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e32513c66bca1e2d1706d50a6615df1a.png)
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9卷引用:甘肃省张掖市某重点校2022-2023学年高三上学期11月月考数学(理)试题
甘肃省张掖市某重点校2022-2023学年高三上学期11月月考数学(理)试题河南省安阳市2022-2023学年高三上学期一轮复习联考(二)全国卷理科数学试题重庆市云阳县高阳中学2023届高三上学期第二次质量检测理科数学试题河北省石家庄市藁城新冀明中学2023届高三一轮复习联考(二)数学试题2023届高三上学期一轮复习联考(二)全国卷理科数学试卷(已下线)专题02 正余弦定理在解三角形中的高级应用与最值问题(精讲精练)-2(已下线)6.4.2 平面向量的应用(精讲)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)第09讲 解三角形中解答题4种基础题型广东省广州市荔湾区西关外国语学校2022-2023学年高一下学期期中数学试题
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解题方法
6 . 函数
的部分图象如图所示.
![](https://img.xkw.com/dksih/QBM/2021/10/21/2834230574768128/2834301581647872/STEM/4f935862-77aa-44a7-9f83-2fd8ca04f0ef.png?resizew=177)
(1)求函数
的解析式;
(2)已知数列
满足
,且
是
与
的等差中项,
①求证:数列
是等比数列;
②求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27cd15ee656d39a864fbecf781f23c5.png)
![](https://img.xkw.com/dksih/QBM/2021/10/21/2834230574768128/2834301581647872/STEM/4f935862-77aa-44a7-9f83-2fd8ca04f0ef.png?resizew=177)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d10a513447f40b5130c7527ae289b2.png)
①求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d17d72d1d20d385920c3d9da6bed8bb.png)
②求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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7 . 已知四边形
内接于圆
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/9/7/2802926345519104/2806605282967552/STEM/4295692976424d4c8e0301d46c9a0e43.png?resizew=126)
(1)求证:
的三边长度可以构成一个等差数列;
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e096f87473d0b6b6d531ba22e5a7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b2f446cccf2652c090e99a75beb3bf.png)
![](https://img.xkw.com/dksih/QBM/2021/9/7/2802926345519104/2806605282967552/STEM/4295692976424d4c8e0301d46c9a0e43.png?resizew=126)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
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2021·全国·模拟预测
8 . 已知
的内角A,B,C的对边分别为a,b,c,且
.
(1)证明:
是等腰三角形;
(2)若
的面积为
,且
,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f585eb57133ed50fdffac8ac0be102.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74632cfc1a161e444040355e7395444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
9 . 已知函数
.把方程
的正数解从小到大依次排成一列,得到数列
,
.
(1)求数列
的通项公式;
(2)记
,设数列
的前
项和为
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89556673cb92c044a892f3fbf79f0a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19f77669fa0060d1e42fbbcb2ec5042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda0c771434b30a909702c34710e89cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e672c3d231081d12e44a4211e5ac60bf.png)
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10 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9c054fac13474dd60bf87a7795eb49.png)
(1)求
的单调区间;
(2)求证曲线
在
上不存在斜率为-2的切线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9c054fac13474dd60bf87a7795eb49.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00f2f6ab162f9333ec55db195d663b.png)
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5卷引用:甘肃省平凉市华亭市第一中学2023-2024学年高三上学期第三次月考数学试卷
甘肃省平凉市华亭市第一中学2023-2024学年高三上学期第三次月考数学试卷北京市八一学校2022届高三10月月考数学试题河南省重点高中2021-2022学年高三下学期阶段性调研联考二文科数学试题河南省郑州市2021届高三三模文科数学试题(已下线)专题02 导数及其应用【知识梳理】-2020-2021学年高二数学下学期期末专项复习(新人教B版2019)