[{"_1":2,"_356":-5,"_357":-5},"loaderData",{"_3":4,"_39":40,"_355":-5},"root",{"_5":6,"_35":36,"_37":38},"allTopics",[7],{"_8":9,"_10":11,"_12":13,"_14":15,"_16":17,"_33":34},"id",2,"title","قدرات عامة","slug","قدرات-عامة","description","اختبار القدرات للمرحلة الثانوية هو اختبار يقيس القدرة على الفهم والتطبيق والاستدلال والتحليل لدى الطالب من خلال اللغة والرياضيات، و معرفة قابلية الطالب للتعلم","metadata",{"_18":19,"_20":19,"_21":19,"_22":19,"_23":19,"_24":19,"_25":19,"_26":19,"_27":19,"_28":19,"_29":19,"_30":19,"_31":19,"_32":19},"support_dynamic_study_plan",true,"study_plan_based_on_section_level","placement_test_based_on_section_level","study_plan_based_on_topic_level","placement_test_based_on_topic_level","question_bank_page","esdarat_page","namathej_page","user_reviews_page","golden_page","study_plan_page","support_exam","data_in_arabic","overview_page","topic_streams",[],"whiteLabelData",{},"isWhitelabeled",false,"routes/_visitor.question.$slug",{"_41":42,"_110":111,"_336":337,"_349":350,"_351":38,"_352":43,"_353":354},"loaderQuestion",{"_8":43,"_44":45,"_46":47,"_10":48,"_12":49,"_50":51,"_52":53,"_54":55,"_56":57,"_58":57,"_59":38,"_60":19,"_61":-5,"_62":63,"_81":82,"_87":88,"_92":93,"_94":38,"_95":-5,"_96":97,"_98":99,"_100":101,"_102":103,"_104":19,"_67":105,"_106":107,"_108":109},46099,"type","MULTIPLE_CHOICE","text","المتطابقة \\ltr{\\csc^2\\theta - \\cot^2\\theta} تكافئ المتطابقة ..","المتطابقة ^2θ- ^2θ تكافئ المتطابقة .. A)cos^2θ+ sin^2θ B)1 - sin^2θ C)1 - cos^2θ D)sin^2θ- cos^2θ ","46099-المتطابقة-تكافئ-المتطابقة","order",32,"unit_id",53,"topic_id",3,"comparison_value1","","comparison_value2","has_text_explanation","has_video_explanation","question_group","question_options",[64,69,73,77],{"_8":65,"_46":66,"_67":68},178890,"\\ltr{\\cos^2\\theta + \\sin^2\\theta}","renderedText"," $\"\"/$ ",{"_8":70,"_46":71,"_67":72},178891,"\\ltr{1 - \\sin^2\\theta}"," $\"\"/$ ",{"_8":74,"_46":75,"_67":76},178892,"\\ltr{1 - \\cos^2\\theta}"," $\"\"/$ ",{"_8":78,"_46":79,"_67":80},178893,"\\ltr{\\sin^2\\theta - \\cos^2\\theta}"," $\"\"/$ ","previous_question",{"_8":83,"_44":45,"_46":84,"_12":85,"_10":-5,"_56":57,"_58":57,"_59":-5,"_60":-5,"_52":-5,"_86":-5,"_54":-5,"_61":-5},46097,"إذا كانت \\ltr{90^\\circ < \\theta < 180^\\circ} و \\ltr{\\cos\\theta = -\\frac{1}{2}} فَأوجد \\ltr{\\sin\\theta}.","46097-إذا-كانت-و-{2}}-فَأوجد-{2}}-}{2}}-{2}}-}{2","section_id","next_question",{"_8":89,"_44":45,"_46":90,"_12":91,"_10":-5,"_56":57,"_58":57,"_59":-5,"_60":-5,"_52":-5,"_86":-5,"_54":-5,"_61":-5},46101,"إذا كانت \\ltr{0^\\circ < \\theta < 90^\\circ} فإن \\ltr{\\sqrt{9 - \\sin^2\\theta - \\cos^2\\theta}} يساوي ..","46101-إذا-كانت-فإن-}-يساوي-}-2","user_video_explanations",[],"has_custom_text_explanation","text_explanation_teaser","total_questions_number",344,"unitTitle","حساب المثلثات","sectionTitle","الرياضيات","sectionId",35,"canExpandImages","المتطابقة $\"\"/$ تكافئ المتطابقة ..","encodedPrevQuestionSlug","46097-%D8%A5%D8%B0%D8%A7-%D9%83%D8%A7%D9%86%D8%AA-%D9%88-%7B2%7D%7D-%D9%81%D9%8E%D8%A3%D9%88%D8%AC%D8%AF-%7B2%7D%7D-%7D%7B2%7D%7D-%7B2%7D%7D-%7D%7B2","encodedNextQuestionSlug","46101-%D8%A5%D8%B0%D8%A7-%D9%83%D8%A7%D9%86%D8%AA-%D9%81%D8%A5%D9%86-%7D-%D9%8A%D8%B3%D8%A7%D9%88%D9%8A-%7D-2","relatedQuestions",[112,141,160,183,205,227,249,271,292,314],{"_8":113,"_44":45,"_46":114,"_12":115,"_10":116,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":57,"_58":57,"_59":38,"_60":19,"_61":-5,"_62":118,"_92":131,"_94":38,"_132":38,"_133":134,"_67":140},45991,"إذا كانت \\ltr{f(\\theta) = \\cos \\theta} والمشتقة الأولى لها هي \\ltr{f'(\\theta) = - \\sin \\theta} وكانت \\ltr{\\sin \\theta = 0.21}، فإن \\ltr{\\sin(\\pi - \\theta)} تساوي ..","45991-%D8%A5%D8%B0%D8%A7-%D9%83%D8%A7%D9%86%D8%AA-%D9%88%D8%A7%D9%84%D9%85%D8%B4%D8%AA%D9%82%D8%A9-%D8%A7%D9%84%D8%A3%D9%88%D9%84%D9%89-%D9%84%D9%87%D8%A7-%D9%87%D9%8A-%D9%88%D9%83%D8%A7%D9%86%D8%AA-%D9%81%D8%A5%D9%86-%D8%AA%D8%B3%D8%A7%D9%88%D9%8A","إذا كانت f(θ) = cosθ والمشتقة الأولى لها هي f (θ) = - sinθ وكانت sinθ= 0.21، فإن sin(π- θ) تساوي .. A)-0.21 B)0 C)0.21 D)0.79 ","unit_name",[119,122,125,128],{"_8":120,"_46":121},178458,"\\ltr{-0.21}",{"_8":123,"_46":124},178459,"\\ltr{0}",{"_8":126,"_46":127},178460,"\\ltr{0.21}",{"_8":129,"_46":130},178461,"\\ltr{0.79}",[],"is_all_explanations_deleted","contents_tags_ids",{"_135":136},"ids",[137,138,139],1554,1557,1563,"إذا كانت $\"\"/$ والمشتقة الأولى لها هي $\"\"/$ وكانت $\"\"/$ ، فإن $\"\"/$ تساوي ..",{"_8":89,"_44":45,"_46":90,"_12":109,"_10":142,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":57,"_58":57,"_59":38,"_60":19,"_61":-5,"_62":143,"_92":156,"_94":38,"_132":38,"_133":157,"_67":159},"إذا كانت 0^∘< θ< 90^∘ فإن √(9 - sin^2θ- cos^2θ) يساوي .. A)2 B)2√(2) C)√(10) D)3 - sinθ- cosθ ",[144,147,150,153],{"_8":145,"_46":146},178898,"2",{"_8":148,"_46":149},178899,"\\ltr{2\\sqrt{2}}",{"_8":151,"_46":152},178900,"\\ltr{\\sqrt{10}}",{"_8":154,"_46":155},178901,"\\ltr{3 - \\sin\\theta - \\cos\\theta}",[],{"_135":158},[137,138],"إذا كانت $\"\"/$ فإن $\"\"/$ يساوي ..",{"_8":161,"_44":45,"_46":162,"_12":163,"_10":164,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":-5,"_58":-5,"_59":38,"_60":19,"_61":-5,"_62":165,"_92":178,"_94":38,"_132":38,"_133":179,"_67":182},46102,"قيمة المحدد\\ltr{\\;\\left|\\;\\begin{array}{cc}\\sin\\;x&\\;\\cos\\;x\\\\-\\cos\\;x\\;&\\sin\\;x\\end{array}\\;\\right|\\;} تساوي ..","46102-%D9%82%D9%8A%D9%85%D8%A9-%D8%A7%D9%84%D9%85%D8%AD%D8%AF%D8%AF-x%26x-x%26x%7D-%D8%AA%D8%B3%D8%A7%D9%88%D9%8A-1-0","قيمة المحدد | [ sin x cos x; -cos x sin x ] | تساوي .. A)0 B)1 C)cos2x D)2 sin^2 x ",[166,169,172,175],{"_8":167,"_46":168},178902,"0",{"_8":170,"_46":171},178903,"1",{"_8":173,"_46":174},178904,"\\ltr{\\cos 2x}",{"_8":176,"_46":177},178905,"\\ltr{2 \\sin^2 x}",[],{"_135":180},[181,138],1545,"قيمة المحدد $\"\"/$ تساوي ..",{"_8":184,"_44":45,"_46":185,"_12":186,"_10":187,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":57,"_58":57,"_59":38,"_60":19,"_61":-5,"_62":188,"_92":201,"_94":38,"_132":38,"_133":202,"_67":204},46104,"القيمة الدقيقة لـ \\ltr{\\sin 15^\\circ} تساوي ..","46104-%D8%A7%D9%84%D9%82%D9%8A%D9%85%D8%A9-%D8%A7%D9%84%D8%AF%D9%82%D9%8A%D9%82%D8%A9-%D9%84%D9%80-%D8%AA%D8%B3%D8%A7%D9%88%D9%8A-%7D%7B4%7D%7D-%2B%7D%7B4%7D%7D-%2B%7D%7B8%7D%7D-%7D%7B2","القيمة الدقيقة لـ sin15^∘ تساوي .. A)√(6)-√(2)/4 B)√(6)+√(2)/4 C)√(6)-√(2)/2 D)√(6)+√(2)/8 ",[189,192,195,198],{"_8":190,"_46":191},178910,"\\ltr{\\frac{\\sqrt{6}-\\sqrt{2}}{4}}",{"_8":193,"_46":194},178911,"\\ltr{\\frac{\\sqrt{6}+\\sqrt{2}}{4}}",{"_8":196,"_46":197},178912,"\\ltr{\\frac{\\sqrt{6}-\\sqrt{2}}{2}}",{"_8":199,"_46":200},178913,"\\ltr{\\frac{\\sqrt{6}+\\sqrt{2}}{8}}",[],{"_135":203},[137,138],"القيمة الدقيقة لـ $\"\"/$ تساوي ..",{"_8":206,"_44":45,"_46":207,"_12":208,"_10":209,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":57,"_58":57,"_59":38,"_60":19,"_61":-5,"_62":210,"_92":223,"_94":38,"_132":38,"_133":224,"_67":226},46106,"القيمة الدقيقة لـ \\ltr{\\cos 75^\\circ} تساوي ..","46106-%D8%A7%D9%84%D9%82%D9%8A%D9%85%D8%A9-%D8%A7%D9%84%D8%AF%D9%82%D9%8A%D9%82%D8%A9-%D9%84%D9%80-%D8%AA%D8%B3%D8%A7%D9%88%D9%8A-%2B-%7D%7B4%7D%7D-%7D%7B2%7D%7D-%2B-%7D%7B8%7D%7D-%7D%7B4","القيمة الدقيقة لـ cos75^∘ تساوي .. A)√(6) - √(2)/4 B)√(6) + √(2)/4 C)√(6) - √(2)/2 D)√(6) + √(2)/8 ",[211,214,217,220],{"_8":212,"_46":213},178918,"\\ltr{\\frac{\\sqrt{6} - \\sqrt{2}}{4}}",{"_8":215,"_46":216},178919,"\\ltr{\\frac{\\sqrt{6} + \\sqrt{2}}{4}}",{"_8":218,"_46":219},178920,"\\ltr{\\frac{\\sqrt{6} - \\sqrt{2}}{2}}",{"_8":221,"_46":222},178921,"\\ltr{\\frac{\\sqrt{6} + \\sqrt{2}}{8}}",[],{"_135":225},[137,138],"القيمة الدقيقة لـ $\"\"/$ تساوي ..",{"_8":228,"_44":45,"_46":229,"_12":230,"_10":231,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":57,"_58":57,"_59":38,"_60":19,"_61":-5,"_62":232,"_92":245,"_94":38,"_132":38,"_133":246,"_67":248},46110,"قيمة \\ltr{\\sin ~15^\\circ ~\\cos~ 45^\\circ - \\cos~ 15^\\circ~ \\sin~ 45^\\circ} تساوي ...","46110-%D9%82%D9%8A%D9%85%D8%A9-%D8%AA%D8%B3%D8%A7%D9%88%D9%8A-%7B2%7D%7D-%7D%7B2%7D%7D-%7D%7B2%7D%7D-%7B2","قيمة sin 15^∘ cos 45^∘- cos 15^∘ sin 45^∘ تساوي ... A)√(3)/2 B)-√(3)/2 C)1/2 D)-1/2 ",[233,236,239,242],{"_8":234,"_46":235},178934,"\\ltr{\\frac{\\sqrt{3}}{2}}",{"_8":237,"_46":238},178935,"\\ltr{-\\frac{\\sqrt{3}}{2}}",{"_8":240,"_46":241},178936,"\\ltr{\\frac{1}{2}}",{"_8":243,"_46":244},178937,"\\ltr{-\\frac{1}{2}}",[],{"_135":247},[137,138],"قيمة $\"\"/$ تساوي ...",{"_8":250,"_44":45,"_46":251,"_12":252,"_10":253,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":57,"_58":57,"_59":38,"_60":38,"_61":-5,"_62":254,"_92":267,"_94":38,"_132":38,"_133":268,"_67":270},46111,"المتطابقة \\ltr{\\cos^4 \\theta - \\sin^4 \\theta} تكافئ المتطابقة ..","46111-%D8%A7%D9%84%D9%85%D8%AA%D8%B7%D8%A7%D8%A8%D9%82%D8%A9-%D8%AA%D9%83%D8%A7%D9%81%D8%A6-%D8%A7%D9%84%D9%85%D8%AA%D8%B7%D8%A7%D8%A8%D9%82%D8%A9","المتطابقة cos^4 θ- sin^4 θ تكافئ المتطابقة .. A)cos4θ B)sin4θ C)cos2θ D)sin2θ ",[255,258,261,264],{"_8":256,"_46":257},178938,"\\ltr{\\cos 4\\theta}",{"_8":259,"_46":260},178939,"\\ltr{\\sin 4\\theta}",{"_8":262,"_46":263},178940,"\\ltr{\\cos 2\\theta}",{"_8":265,"_46":266},178941,"\\ltr{\\sin 2\\theta}",[],{"_135":269},[138],"المتطابقة $\"\"/$ تكافئ المتطابقة ..",{"_8":272,"_44":45,"_46":273,"_12":274,"_10":275,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":57,"_58":57,"_59":38,"_60":19,"_61":-5,"_62":276,"_92":288,"_94":38,"_132":38,"_133":289,"_67":291},46112,"إذا علمت أن \\ltr{0^\\circ \\leq \\theta \\leq 90^\\circ} و \\ltr{\\tan \\theta = 0} فإن القيمة الدقيقة ل \\ltr{\\tan 2\\theta} تساوي..","46112-%D8%A5%D8%B0%D8%A7-%D8%B9%D9%84%D9%85%D8%AA-%D8%A3%D9%86-%D9%88-%D9%81%D8%A5%D9%86-%D8%A7%D9%84%D9%82%D9%8A%D9%85%D8%A9-%D8%A7%D9%84%D8%AF%D9%82%D9%8A%D9%82%D8%A9-%D9%84-%D8%AA%D8%B3%D8%A7%D9%88%D9%8A-%7D%7B2","إذا علمت أن 0^∘≤θ≤90^∘ و tanθ= 0 فإن القيمة الدقيقة ل tan2θ تساوي.. A)0 B)1 C)√(2)2 D)2 ",[277,279,282,285],{"_8":278,"_46":124},178942,{"_8":280,"_46":281},178943,"\\ltr{1}",{"_8":283,"_46":284},178944,"\\ltr{\\dfrac{\\sqrt{2}}{2}}",{"_8":286,"_46":287},178945,"\\ltr{2}",[],{"_135":290},[137,138],"إذا علمت أن $\"\"/$ و $\"\"/$ فإن القيمة الدقيقة ل $\"\"/$ تساوي..",{"_8":293,"_44":45,"_46":294,"_12":295,"_10":296,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":57,"_58":57,"_59":38,"_60":19,"_61":-5,"_62":297,"_92":310,"_94":38,"_132":38,"_133":311,"_67":313},46115,"إذا علمنا أن \\ltr{0^\\circ < \\theta < 90^\\circ} و \\ltr{\\cos \\theta = \\frac{\\sqrt{3}}{2}} فإن قيمة \\ltr{\\tan \\frac{\\theta}{2}} تساوي ...","46115-%D8%A5%D8%B0%D8%A7-%D8%B9%D9%84%D9%85%D9%86%D8%A7-%D8%A3%D9%86-%D9%88-%7D%7B2%7D%7D-%D9%81%D8%A5%D9%86-%D9%82%D9%8A%D9%85%D8%A9-%7B2%7D%7D-%D8%AA%D8%B3%D8%A7%D9%88%D9%8A-%7D%7B3%7D%7D-%7D%7D-2","إذا علمنا أن 0^∘< θ< 90^∘ و cosθ= √(3)/2 فإن قيمة tanθ/2 تساوي ... A)√(7 - 4√(3)) B)√(3) - 2 C)√(3)/3 D)√(3) ",[298,301,304,307],{"_8":299,"_46":300},178954,"\\ltr{\\sqrt{7 - 4\\sqrt{3}}}",{"_8":302,"_46":303},178955,"\\ltr{\\sqrt{3} - 2}",{"_8":305,"_46":306},178956,"\\ltr{\\frac{\\sqrt{3}}{3}}",{"_8":308,"_46":309},178957,"\\ltr{\\sqrt{3}}",[],{"_135":312},[137,138],"إذا علمنا أن $\"\"/$ و $\"\"/$ فإن قيمة $\"\"/$ تساوي ...",{"_8":315,"_44":45,"_46":316,"_12":317,"_10":318,"_52":53,"_117":-5,"_54":55,"_86":103,"_56":57,"_58":57,"_59":38,"_60":19,"_61":-5,"_62":319,"_92":332,"_94":38,"_132":38,"_133":333,"_67":335},46119,"قيمة \\ltr{\\sin^{-1} (\\cos 72^\\circ)} تساوي ..","46119-%D9%82%D9%8A%D9%85%D8%A9-(-72%5E)%7D-%D8%AA%D8%B3%D8%A7%D9%88%D9%8A","قيمة sin^-1 (cos72^∘) تساوي .. A)72^∘ B)18^∘ C)38^∘ D)108^∘ ",[320,323,326,329],{"_8":321,"_46":322},178970,"\\ltr{72^\\circ}",{"_8":324,"_46":325},178971,"\\ltr{18^\\circ}",{"_8":327,"_46":328},178972,"\\ltr{38^\\circ}",{"_8":330,"_46":331},178973,"\\ltr{108^\\circ}",[],{"_135":334},[137,138],"قيمة $\"\"/$ تساوي ..","detailedAnswer",[338,343,345,347],{"_8":65,"_46":66,"_339":19,"_340":341,"_342":-5},"is_correct","question_option_details",[],"has_access",{"_8":70,"_46":71,"_339":38,"_340":344,"_342":-5},[],{"_8":74,"_46":75,"_339":38,"_340":346,"_342":-5},[],{"_8":78,"_46":79,"_339":38,"_340":348,"_342":-5},[],"imagesURLs",[],"isMobile","questionId","streamId",1,"routes/_visitor","actionData","errors"]

المتطابقة تكافئ المتطابقة ..

المتطابقة $\ltr{\csc^2\theta - \cot^2\theta}$ تكافئ المتطابقة ..