名校
解题方法
1 . 已知锐角
中,角
,
,
所对的边分别为
,
,
,其中
,
,且
.
(1)求证:
;
(2)已知点
在线段
上,且
,求
的取值范围.
![](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/36e15cbd7c42d7b15d7ba8d2b28ab8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084399e0edc1c3bfb33b338987dcfa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098943e98ad321740f83f0bb67004598.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f44c181a2f6ae22d5d52b374768dc57.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eab3edfe4687c78c290b7e7e5e0cbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
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2024-05-11更新
|
1193次组卷
|
3卷引用:宁夏回族自治区石嘴山市第一中学2023-2024学年高一下学期5月期中数学试题
名校
2 . 如图所示,在△ABC中,点D是边BC的中点,点E是线段上靠近A的一个三等分点,过点E的直线与边AB,AC分别交于点P,Q.设
,
,其中
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ce10d13e84bc67c1a12f0acd35d9d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/a39fda62-9563-45f7-b5dc-c1e1bc04ea7a.png?resizew=128)
(1)求证:
为定值,并求此定值;
(2)设△APQ的面积为
,△ABC的面积为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a96f93c74e45318dab2ef44893ad687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e20b752572a7e0ab2e32e4a93a8c8f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ce10d13e84bc67c1a12f0acd35d9d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/a39fda62-9563-45f7-b5dc-c1e1bc04ea7a.png?resizew=128)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(2)设△APQ的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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2022-10-29更新
|
654次组卷
|
2卷引用:宁夏六盘山高级中学2023届高三(提升班)上学期期中考试数学(文)试题
名校
解题方法
3 . 在斜三棱柱
中,底面是边长为4的正三角形,
,
.
平面
;
(2)证明:
;
(3)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c3a693e8339e34c6f15f72a1aae75e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26208e5d58cc5abf1af936480d1932b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f647de53756993a680347e8ce3c0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eacc0e7474802ce634de6f55a3287115.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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2022-07-02更新
|
621次组卷
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3卷引用:宁夏银川市第二中学2022-2023学年高一下学期期中考试数学试题
名校
4 . 记
的内角A,B,C的对边分别为a,b,c,已知
.
(1)证明:
;
(2)当
时,求
的面积S.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e289885f61af21a6a78d68cd1e7588c2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa8d75a6638e08eedbff8662267da6f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76f303c572e65dce9aa819102c75b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2022-04-21更新
|
2136次组卷
|
3卷引用:宁夏石嘴山市第三中学2022-2023学年高三上学期中考试数学试题(理科)
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5 . 如图,
是平面四边形
的一条对角线,已知
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/f482ed50-9b3d-466e-b5be-9c9671bb8e13.png?resizew=185)
(1)求证:
为等腰直角三角形;
(2)若
,
,求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4355c3b7f9a75c91aae33d869f0350b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dcc535649e4f8c842a63d724bfd8cc9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/f482ed50-9b3d-466e-b5be-9c9671bb8e13.png?resizew=185)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb961bd7db3adb76af2d4cedb611bd7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2020-02-15更新
|
488次组卷
|
3卷引用:宁夏银川市第二中学2022-2023学年高一下学期期中考试数学试题
名校
6 . 某同学再一次研究性学习中发现,以下三个式子的值都等于一个常数.
①.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc285f3defa0a4920c042358be0e328d.png)
②.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a99001d0c1fb5e8c051bec66c6af675.png)
③.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a2ff35686612ef252f2737f8561ee88.png)
(1)试从上述三个式子中选出一个计算出这个常数.
(2)猜想出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/fc285f3defa0a4920c042358be0e328d.png)
②.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a99001d0c1fb5e8c051bec66c6af675.png)
③.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a2ff35686612ef252f2737f8561ee88.png)
(1)试从上述三个式子中选出一个计算出这个常数.
(2)猜想出反映一般规律的等式,并对等式的正确性作出证明.
您最近一年使用:0次
2019-08-02更新
|
557次组卷
|
5卷引用:宁夏吴忠市吴忠中学2021-2022学年高一下学期期中考试数学试题
宁夏吴忠市吴忠中学2021-2022学年高一下学期期中考试数学试题四川省南充市西华师范大学附属中学2022-2023学年高一下学期期中考试数学试题内蒙古赤峰市2018-2019学年高二下学期期末联考数学(文)试题四川省遂宁市遂宁中学校2021-2022学年高一下学期3月月考数学试题(已下线)专题5-5 三角函数综合大题归类(1) - 【巅峰课堂】题型归纳与培优练
13-14高二下·宁夏银川·期中
解题方法
7 . 如图,设有双曲线
,F1,F2是其两个焦点,点M在双曲线上.
(1)若∠F1MF2=90°,求△F1MF2的面积.
(2)若∠F1MF2=60°,△F1MF2的面积是多少?若∠F1MF2=120°,△F1MF2的面积又是多少?
(3)观察以上计算结果,你能看出随∠F1MF2的变化,△F1MF2的面积将怎样变化吗?试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f8ae565db8a7d4b95fdd85e28afa2f.png)
(1)若∠F1MF2=90°,求△F1MF2的面积.
(2)若∠F1MF2=60°,△F1MF2的面积是多少?若∠F1MF2=120°,△F1MF2的面积又是多少?
(3)观察以上计算结果,你能看出随∠F1MF2的变化,△F1MF2的面积将怎样变化吗?试证明你的结论.
![](https://img.xkw.com/dksih/QBM/2014/6/16/1571776987750400/1571776993591296/STEM/6ff54d211337416cbd2e538db49a43c9.png?resizew=138)
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