diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 73bcb9ed..df32e6e9 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -49336,7 +49336,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024720" + ], "remark": "", "space": "4em", "unrelated": [] @@ -684181,6 +684183,56 @@ "space": "", "unrelated": [] }, + "024719": { + "id": "024719", + "content": "在$\\triangle ABC$中, 若$\\cos 2B-\\cos 2C=2\\sin ^2A$, 则此三角形的形状为\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "直角三角形", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷05小测-20240311修改", + "edit": [ + "20230324\t王伟叶", + "20240311\t吴轩萍" + ], + "same": [], + "related": [ + "040253" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024720": { + "id": "024720", + "content": "已知$\\sin 2\\alpha=-\\dfrac{8}{17}$, 且$\\pi<2\\alpha<\\dfrac{3\\pi}{2}$, 则$\\tan\\alpha=$\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t2115-万能置换公式与半角公式-20240311修改", + "edit": [ + "20220625\t王伟叶", + "20240311\t吴轩萍" + ], + "same": [], + "related": [ + "001473" + ], + "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