山西省九年级2023-2024学年新课标闯关卷（四）SHX数学.试卷答案,我们目前收集并整理关于山西省九年级2023-2024学年新课标闯关卷（四）SHX数学.得系列试题及其答案，更多试题答案请关注微信公众号：趣找答案/直接访问www.qzda.com(趣找答案)

山西省九年级2023-2024学年新课标闯关卷（四）SHX数学.试卷答案

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32.WhatcanbeleamedabouttheMilkyWay?氏化《，扩两共照明彩词代前二A.Thecenterofitremainsunknown.B.Thesunisn'tlocatedinthecenterofit.C.Itscenterisverypeaceful.D.Itscenterfeaturesfewerstars.33.What'sparagraph2mainlyabout?A.Thecollectionofspacedata.B.Thedifferencesofspacewaves.C.Theformationofthenewimage.D.ThefunctionoftheMeerKATtelescope.34.Whatcanweknowaboutthegasessentoubytheblackhole?A.Theywillformsuperbigmatter.B.TheywillabsorbsurroundingmaterialsC.Theygetbentifawayfromtheirsource.D.Theyarelikelytoexplodewhensuperheated.35.Whatmaybethebesttitleforthetext?A.OurGalaxy'sViolentHeartB.AnAttempttoTravelinOuterSpaceC.Stars'PurpleStreaksD.RadioWavesfromOuterSpace第二节（共5小题：每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填人空白处的最佳选项

选项中有两项为多余选项

Youalwayshopetoreceivesupportorcomfortfromyourfriendswhenyoufeeldown.Yourfriendsfeelthesameway.However,itmaybenoteasytocheerupyourfriendswhenyoucan'tbebytheirside.36Askifthere'sanythingyoucandotohelp.Differentpeopleprefertobecomfortedindifferentways.Askifthere'sanythingspecificyoucandotohelpyourfriends.37Whileyou'retalkingonthephone.saysomethinglike,"WhatcanIdotohelp?I'malwayshereifyouneedanything."38Thissimplegesturecanreallybrightenyourfriends'day.Ifyourfriendsareinneedofcomfort.sendthemfrequentremindersthatyou'rethinkingofthem.Sharesomethingthatremindedyouofthem.Itwillletyourfriendsknowthatthey'restillimportantinyourlifeevenifthey'refaraway.Listwhyyouthinkthey'respecial.39Sendthemalistofallthereasonswhyyouthinkthey'reamazing.Whetheritmaybetheirkindandcompassionate(富有同t情心的)nature,theirsenseofstyle,ortheirpowertofindthecoolestmusic.tellthemwhyyouaresogratefultoknowthem.Afterreadingwhatyouhavelisted.theywillfeelencouraged.Sendthemagift.Surprisethemwithsomethingspecialtomaketheirday.Arrangeforflowerstobedeliveredtotheirapartmentormailthemoneoftheirfavoritealbums.40Ahomemadegift.likeaknitted()scarforapieceofartwork,willlifttheirspiritsallthesame.A.Sendagifttothemtocelebratetheirsuccess.B.Thankfully.therearemanywaysyoucanhelp.C.Therefore.youcanvisitthemtocheerthemup.D.Textthemtoletthemknowthey'reonyourmind.E.Youdon'thavetogoalloutintermsofspending.F.Ifthey'vebeendownonthemselveslately,theymayneedareminder.G.Thequestionowillshowyoucreandtheywillappreciateyourkindoffer.【23模拟调研·英语（一）第6页（共8页）11Y】

分析（1）由条件利用同角三角函数基本关系式，两角和的余弦函数公式，倍角公式化简即可证明．
（2）由条件利用两角和差的正弦公式、同角三角函数的基本关系可得2tanβ•tan²α-tanα+tanβ=0，再根据△=1-8tan²β≥0，求得tanβ的最大值．

解答解：（1）证明：$\frac{sinβ}{sinα}$=cos（α+β），其中α，β为锐角．
⇒sinβ=sinα（cosαcosβ-sinαsinβ）
⇒sinβ（1-sin²α）=$\frac{1}{2}$sin2αcosβ
⇒tanβ=$\frac{sin2α}{2+2×\frac{1-cos2α}{2}}$=$\frac{sin2α}{3-cos2α}$．
得证．
（2）解：角α，β为锐角，且cos（α+β）sinα=sinβ=sin[（α+β）-α]，
∴cos（α+β）sinα=sin（α+β）cosα-cos（α+β）sinα，
化简可得tan（α+β）=2tanα，即$\frac{tanα+tanβ}{1-tanαtanβ}$=2tanα，
故有2tanβ•tan²α-tanα+tanβ=0，∴△=1-8tan²β≥0，
求得-$\frac{\sqrt{2}}{4}$≤tanβ≤$\frac{\sqrt{2}}{4}$，β为锐角，故0＜tanβ≤$\frac{\sqrt{2}}{4}$．
故tanβ的最大值是：$\frac{\sqrt{2}}{4}$．

点评本题主要考查两角和差的正弦公式，余弦函数公式，倍角公式，同角三角函数的基本关系的应用，考查了计算能力和转化思想，属于基础题．

山西省九年级2023-2024学年新课标闯关卷（四）SHX数学.