1 . 已知
中,内角
、
、
的对边分别为
、
、
,且
.
(Ⅰ)求证:
、
、
成等差数列;
(Ⅱ)求函数
取得最大值时角
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/f0ad7060a5591a0cc7d9e596ea76cb08.png)
(Ⅰ)求证:
![](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)
(Ⅱ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3b026a73452f5c358e01b51adc3191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2 . 已知
中,内角
、
、
的对边为
、
、
,
三角形
外接圆的半径,证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34369422d71dd95c61cdd1b8245d7b6c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30b12f8bf54428846cf378ffd5a23b7.png)
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3 . 通常用
分别表示△ABC的三个内角A、B、C所对的边的长度,R表示△ABC外接圆半径.
(1)在以O为圆心,半径为2的圆O中,BC和BA是圆O的弦,其中BC=2,∠ABC=45°,求弦AB的长;
(2)在△ABC中,若∠C是钝角,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
(1)在以O为圆心,半径为2的圆O中,BC和BA是圆O的弦,其中BC=2,∠ABC=45°,求弦AB的长;
(2)在△ABC中,若∠C是钝角,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367961102740219545901df94d226ad2.png)
您最近一年使用:0次
名校
解题方法
4 . 在
中,角
,
,
所对的边分别为
,
,
,且
.
(1)求证:
;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/f296989add06c4bc2207a20b0746e533.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff7989c371fc6dd1627bdb88fcb917d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b9446d7b31f0d6e044cf99deeb20aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5201fc26d013f6fb889933c0e32f5c53.png)
您最近一年使用:0次
5 .
的内角的对边
分别为
.
(1)求证:
;
(2)在边
上取一点P,若
.求证:
.
![](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)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52bd9362c24922a2a3af255fac9bbfe2.png)
(2)在边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad46f23c0313f49d9bc1fec0e9641612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8580839def5eb012fce630d4fa50eb.png)
您最近一年使用:0次
6 . 在
中,两直角边AB,AC的长分别为m,n(其中
),以BC的中点O为圆心,作半径为r(
)的圆O.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/7a7d69a4-47ff-4577-8836-ed1e09c175e3.png?resizew=187)
(1)若圆O与
的三边共有4个交点,求r的取值范围;
(2)设圆O与边BC交于P,Q两点;当r变化时,甲乙两位同学均证明出
为定值甲同学的方法为:连接AP,AQ,AO,利用两个小三角形中的余弦定理来推导;乙同学的方法为;以O为原点建立合适的直角坐标系,利用坐标法来计算.请在甲乙两位同学的方法中选择一种来证明该结论,定值用含m、n的式子表示.(若用两种方法,按第一种方法给分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5ae4101c20f367ff95e41e58ce638b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/7a7d69a4-47ff-4577-8836-ed1e09c175e3.png?resizew=187)
(1)若圆O与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)设圆O与边BC交于P,Q两点;当r变化时,甲乙两位同学均证明出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b7688d9d4e794a832e655f74de95e94.png)
您最近一年使用:0次
7 . 证明三角形
的面积公式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7990ee0a6f7bb09543e3abd1202b76.png)
您最近一年使用:0次
2020-02-03更新
|
302次组卷
|
2卷引用:人教A版(2019) 必修第二册 逆袭之路 第六章 6.4 平面向量的应用 小结
8 .
中,三内角
所对的边分别为
,已知
成等差数列.
(Ⅰ)求证:
;
(Ⅱ)求角
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/2f81b8a02e231884bc36fdc4870830cc.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a95735ae1e71fcfc71f244b92ddb52c.png)
(Ⅱ)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
2019-07-01更新
|
739次组卷
|
2卷引用:江西省九江市2018-2019学年高二下学期期末数学(理)试题
9 . 在
中,角
所对的边分别为
.
(1)若
为
边的中点,求证:
;
(2)若
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea49e8abfc92cb54c73539c09541309b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79017fd0fd57bdc170b917b4e20f4c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
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10 .
的内角A,B,C所对的边分别为a,b,c.已知
.
(1)证明:
;
(2)若
,
的面积为
,求a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f040bc7ae944d978f499917a3949e0.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64afdc6fcdc4cd326bb11679766c223e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5742b2684d00be50a66e01c9acb6b51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
您最近一年使用:0次
2019-10-29更新
|
681次组卷
|
2卷引用:“四省八校”2019-2020学年高三第一次教学质量检测数学(文)试题1