名校
解题方法
1 . 在
中,角
的对边分别为
,已知
.
(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/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d945c75c4507b2fd2b42493fa8db59df.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cb21ae875f36d52d0b6f82b0201d0e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436e566dcc65889d01c7ea9453530b78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2023-04-21更新
|
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2卷引用:吉林省长春市第二中学2022-2023学年高三下学期第七次调研测试数学试卷
2 . 在正项数列
中,
,
.
(1)求
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fede0eb854f39a53fb01c4fc5060fa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a571aa47a61706758aa2f16ba9f56f2.png)
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4卷引用:吉林省长春市2023届高三三模数学试题
3 . 记
的内角
、
、
的对边分别为
、
、
,已知
.
(1)证明:
;
(2)若
,
,角
的内角平分线与边
交于点
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/157d2f0f0db718649f148134436c3a43.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428d8ba5d74557ac0660343e61b3bd8f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9597cc64469c379d47dfc6b3f27feee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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3卷引用:吉林省长春市十一高中2022-2023学年高一下学期第二学程考试数学试题
名校
解题方法
4 . 已知等差数列
满足
,
,
的前n项和为
.
(1)求
及
的通项公式;
(2)记
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0939caf47d751f8c7139bd0b25fe98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5775fff251847305756b90e62429f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1339f4e85f82a007362def9c8a31237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762022cd7c3133845e5f6c5cbb6c536c.png)
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3卷引用:吉林省长春市长春外国语学校2022-2023学年高三上学期期末数学试题
名校
解题方法
5 . 已知
,
,
分别为
三个内角
,
,
的对边,
.
(1)求证:
是等腰三角形;
(2)若
,
的面积为
,求
的值.
![](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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e65f3ca149022d8a0ee5f70e9fa776.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3320a13248a3a1208ff6ee85c9d26f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbff61fe9d4e93d7cc338489d1c99c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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6 . 在△ABC中,内角A,B,C的对边分别为a,b,c.从下面①②③中选取两个作为条件,证明另外一个成立.
①
;②
;③
.
注:若选择不同的组合分别解答,则按第一个解答计分.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765ff3b58624701511f4120b2f48cfca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4c86001d89a2c26844074df7d35a7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0f8cec0bda89b6c2ad7ab3cd6c219c.png)
注:若选择不同的组合分别解答,则按第一个解答计分.
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4卷引用:东北三省三校2023届高三第一次联合模拟考试数学试题
(已下线)东北三省三校2023届高三第一次联合模拟考试数学试题东北三省三校2023届高三第一次联合模拟考试数学试题(已下线)东北三省三校2023届高三第一次联合模拟考试数学试题山东省淄博市2023-2024学年高三上学期期中数学试题
7 . 在△ABC中,角A,B,C的对边分别为a,b,c.已知
.
(1)证明:
.
(2)若D为BC的中点,从①
,②
,③
这三个条件中选取两个作为条件证明另外一个成立.
注:若选择不同的组合分别解答,则按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6278ffaf42642fb0f452fd300b09e0d5.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
(2)若D为BC的中点,从①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45373166e0a004b3b4d910655d409b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
注:若选择不同的组合分别解答,则按第一个解答计分.
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|
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16卷引用:吉林省长春市新解放学校2022-2023学年高一下学期第一次月考数学试题
吉林省长春市新解放学校2022-2023学年高一下学期第一次月考数学试题湖南省部分校2022-2023学年高一下学期第一次阶段性诊断考试数学试题广西2023届高三模拟考试数学(理)试题福建省福州第十八中学2022-2023学年高一下学期期中考试数学试题广西壮族自治区玉林市2023届高三二模数学(文)试题广西壮族自治区玉林市2023届高三二模数学(理)试题(已下线)专题06三角函数与解三角形(解答题)(已下线)专题06三角函数与解三角形(解答题)黑龙江省哈尔滨市第六中学校2022-2023学年高一下学期期中数学试题黑龙江省双鸭山市第一中学2022-2023学年高一下学期期末数学试题青海省西宁北外附属新华联外国语高级中学2022-2023学年高一下学期第一次月考数学试题(已下线)专题08 解三角形-1黑龙江省双鸭山市第一中学2023-2024学年高一上学期期中数学试题河南省焦作市第十一中学2022-2023学年高一下学期4月月考数学试题(已下线)广西南宁市横县2023-2024学年高一下学期4月考试数学试题吉林省白山市第一中学2023-2024学年高一下学期6月月考数学试题
8 . 已知数列
满足
,
.
(1)证明:数列
是等差数列,并求数列
的通项公式;
(2)设数列
的前n项的积为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222fba22f5b2f01555df114c422ce993.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3e74fcd0b38bb7bbe6f0d8d2d4a256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b435276754f14e88584ac67243be69cc.png)
您最近一年使用:0次
名校
解题方法
9 . 已知各项均为正数的数列
的前
项和为
,且
,
,
成等差数列.
(1)证明:数列
是等比数列,并写出数列
的通项公式;
(2)若
,设
,求数列
的前
项和
.
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b0f4c4bb231801fc88b28f05c10ec8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b67af73f586837594ab0db4b89baed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
解题方法
10 . 已知正项数列
的前n项和为
,
.
(1)求数列
的通项公式;
(2)设
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768c850421989c8a4bccbdaca4e3bc69.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f128819d216f23d0266882fe5b4cb0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d76c3eb0a07a827877d7a4dc306211.png)
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|
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7卷引用:吉林省长春市东北师范大学附属中学2022-2023学年高二下学期期末数学试题