收录高三寒假作业23新题

工具v2/文本文件/新题收录列表.txt

@@ -67,3 +67,6 @@
 20240125-105348
 023789:023798
 
+20240125-105739
+023799:023805,003102,023806:023807
+

题库0.3/Problems.json

@@ -48008,7 +48008,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023803"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -233127,7 +233129,9 @@
             "20220726\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023807"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -335545,7 +335549,9 @@
             "20221117\t朱敏慧\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023805"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -581539,7 +581545,9 @@
             "20230209\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023800"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -642405,6 +642413,200 @@
         "space": "4em",
         "unrelated": []
     },
+    "023799": {
+        "id": "023799",
+        "content": "若 $\\cot (\\pi-\\alpha)=2$, 则 $\\cos (\\dfrac{3 \\pi}{2}+2 \\alpha)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023800": {
+        "id": "023800",
+        "content": "若 $\\dfrac{3}{2}\\pi<\\alpha<\\dfrac{5}{2}\\pi$, 则 $\\sqrt{\\dfrac{1}{2}+\\dfrac{1}{2}\\sqrt{\\dfrac{1}{2}+\\dfrac{1}{2}\\cos \\alpha}}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "040122",
+            "040232",
+            "021598"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023801": {
+        "id": "023801",
+        "content": "已知 $\\sin \\alpha=\\dfrac{4}{5}$, $\\cos (\\alpha+\\beta)=-\\dfrac{3}{5}$, 若 $\\alpha$、$\\beta$ 都是第一象限的角, 则 $\\sin \\beta=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "040091"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023802": {
+        "id": "023802",
+        "content": "若 $\\sin \\theta, \\cos \\theta$ 是二次方程 $2 x^2-(\\sqrt{3}+1) x+m=0$ 的两个根, 则 $\\dfrac{\\sin \\theta}{1-\\cot \\theta}+\\dfrac{\\cos \\theta}{1-\\tan \\theta}$ 的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023803": {
+        "id": "023803",
+        "content": "若 $\\alpha+\\beta=\\dfrac{\\pi}{3}$, 则 $\\tan \\alpha+\\tan \\beta+\\sqrt{3}\\tan \\alpha \\tan \\beta=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "001435"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023804": {
+        "id": "023804",
+        "content": "化简: $\\cos (20^{\\circ}+x) \\cos (25^{\\circ}-x)-\\cos (70^{\\circ}-x) \\sin (25^{\\circ}-x)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023805": {
+        "id": "023805",
+        "content": "已知 $\\tan (\\dfrac{\\pi}{4}+\\theta)=3$, 则 $\\sin 2 \\theta-2 \\cos ^2 \\theta$ 的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "012059",
+            "040353"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023806": {
+        "id": "023806",
+        "content": "若表达式 $3 \\sin ^2 \\theta+\\sqrt{3}\\sin \\theta \\cos \\theta+4 \\cos ^2 \\theta+k$ 可化为 $\\sin (2 \\theta+\\varphi)$, $0 \\leq \\varphi<2 \\pi$ 的形式, 则 $k$ 的值为\\blank{50}, $\\varphi$ 的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023807": {
+        "id": "023807",
+        "content": "已知 $\\tan \\alpha, \\tan \\beta$ 是方程 $x^2+a x+a+1=0$ 的两个实根, 求证: $\\sin (\\alpha+\\beta)=\\cos (\\alpha+\\beta)$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "008176",
+            "040340"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
@@ -700359,7 +700561,9 @@
             "20230302\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023801"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -701075,7 +701279,9 @@
         "same": [
             "040232"
         ],
-        "related": [],
+        "related": [
+            "023800"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -704243,7 +704449,9 @@
         "same": [
             "040122"
         ],
-        "related": [],
+        "related": [
+            "023800"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -707011,7 +707219,9 @@
             "20230326\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023807"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -707298,7 +707508,9 @@
             "20230326\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023805"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []