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［广东大联考］广东省2023-2024学年度高二年级上学期期中考试（10月）数学.试卷答案

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高考复习（ZJZ)第22期综合能力评估试题(16)参考答案及部分解析参考答案1-5CCBAA6-10BABCA11-15BACBB16-20AABCC21-25CBDBA26-30DCBDA31-35BDCBA36-40DCGAF41-45DBCBA46-50DDAAB51-55CBACD56.than57.of58.trapping59.investigated60.isproduced61.successfully62.a63.toturn64.achievement65.effective写作第一节Onepossibleversion:DearChris,It'sgreattoreceiveyourlastemail.I'mfairlypleasedtolearnthatyouhavewonfirstprizeintheshortvideocontestforoverseasstudentsheldbyourcity.I'mwritingtooffermycongratulationstoyou.Itcameasnosurprisetomethatyouwonfirstprize,because,asIknow,youhaveatalentformakingshortvideosandhavemadeeveryefforttopracticemakingtheminyoursparetime.I'msogladthatyourconstanteffortfinallypaidoffandyourpersistencewasawarded.Congratulationsagainonyoursuccess!Yours,LiHua第二节Onepossibleversion:PootPootlikestositonAtlas'backwhensheliesonthefloortoreadduringhomeschoolingAndhealwayswaveshislittletailhearingAtlas'voice.WhateverAtlasdoes,hedoes:watchingTV,playing,orsleeping.HelovestoplaywithAtlasandthechickens,evenstandingontopofourdogswhentheylieonthefloor.Now,weighinginattenpounds,PootPoothashisownareaoutside.Hehasanewfriend,atwo-month-oldgoatnamedDotsy,whoisalreadythesamesizeashim.WheneverAtlasstepsfootoutsidethedoor,PootPootscreamsuntilshecomesovertogethim.AtlaspicksstrawberriesandbeansfromthegardenforPootPootandherself.Theonlythinghelovesmoreisdeliciouscheeseballs.Thepairoftenplayhide-and-seekinthetallgrass,AtlaswaitinguntilPootPootturnsaround,thenrunningawaytohide,PootPootcryingandjoggingashefollowsthesoundofhervoice.Thislittlekidhasalreadybroughtsomuchjoyintoourlivesandhasbecomeaspecialpartofourfamily部分解析阅读

分析由条件利用同角三角函数的基本关系、二倍角公式化简所给的式子，证明2sin²α•sin²β+2cos²α•cos²β-cos2α•cos2β=1即可．

解答解：∵cos2αcos2β=（cos²α-sin²α）（cos²β-sin²β）
=cos²αcos²β-cos²αsin²β-sin²αcos²β+sin²αsin²β，
∴2sin²α•sin²β+2cos²α•cos²β-cos2α•cos2β
=2sin²α•sin²β+2cos²α•cos²β-（cos²αcos²β-cos²αsin²β-sin²αcos²β+sin²αsin²β）
=cos²α•cos²β+sin²α•sin²β+cos²αsin²β+sin²αcos²β
=（cos²α•cos²β+cos²αsin²β）+（sin²α•sin²β+sin²αcos²β）
=cos²α+sin²α=1，
故得证．

点评本题主要考查同角三角函数的基本关系、二倍角公式的应用，属于中档题．

［广东大联考］广东省2023-2024学年度高二年级上学期期中考试（10月）数学.