添加三道关联题

题库0.3/Problems.json

@@ -48801,7 +48801,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024618"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -680686,6 +680688,81 @@
         "space": "",
         "unrelated": []
     },
+    "024618": {
+        "id": "024618",
+        "content": "将下列各式写成$A\\sin(\\alpha+\\varphi)$的形式, 其中$A>0$, $\\varphi\\in [-\\pi,\\pi)$.\\\\ \n(1) $\\cos\\alpha+\\sin\\alpha=$\\blank{100};\\\\ \n(2) $\\sqrt{3}\\sin\\alpha-\\cos\\alpha=$\\blank{100};\\\\ \n(3) $\\cos\\alpha-\\sqrt{3}\\sin\\alpha=$\\blank{100};\\\\ \n(4) $3\\sin\\alpha+4\\cos\\alpha=$\\blank{100}, 其中$\\varphi$满足\\blank{100};\\\\ \n(5) $12\\sin\\alpha-5\\cos\\alpha=$\\blank{100}, 其中$\\varphi$满足\\blank{100}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t2113-辅助角公式-20240304修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20240304\t徐慧"
+        ],
+        "same": [],
+        "related": [
+            "001453"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024619": {
+        "id": "024619",
+        "content": "求值: $\\tan 36^{\\circ}+\\sqrt{3} \\tan 24^{\\circ} \\tan 36^{\\circ}+\\tan 24^{\\circ}$.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "4em",
+        "ans": "$\\sqrt{3}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷04-20240304修改",
+        "edit": [
+            "20230308\t王伟叶",
+            "20240304\t徐慧"
+        ],
+        "same": [],
+        "related": [
+            "040188"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024620": {
+        "id": "024620",
+        "content": "化简: $\\cos 12^{\\circ} \\cos 24^{\\circ} \\cos 48^{\\circ} \\cos 96^{\\circ}$.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "4em",
+        "ans": "$-\\dfrac1{16}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05-20240304修改",
+        "edit": [
+            "20230318\t王伟叶",
+            "20240304\t徐慧"
+        ],
+        "same": [],
+        "related": [
+            "040228"
+        ],
+        "remark": "",
+        "space": "",
+        "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.",
@@ -743102,7 +743179,9 @@
         "same": [
             "001438"
         ],
-        "related": [],
+        "related": [
+            "024619"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -744193,7 +744272,9 @@
         "same": [
             "040118"
         ],
-        "related": [],
+        "related": [
+            "024620"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []