新高考數(shù)學(xué)一輪復(fù)習(xí)第4章 第03講 兩角和與差的正弦、余弦和正切公式 精講+精練（學(xué)生版）

第03講兩角和與差的正弦、余弦和正切公式(精講+精練）目錄第一部分：知識點(diǎn)精準(zhǔn)記憶第二部分：課前自我評估測試第三部分：典型例題剖析高頻考點(diǎn)一：公式的基本應(yīng)用高頻考點(diǎn)二：公式的逆用及變形高頻考點(diǎn)三：輔助角公式的運(yùn)用高頻考點(diǎn)四：二倍角高頻考點(diǎn)五：拼湊角第四部分：高考真題感悟第五部分：第03講兩角和與差的正弦、余弦和正切公式（精練）第一部分：知識點(diǎn)精準(zhǔn)記憶第一部分：知識點(diǎn)精準(zhǔn)記憶1、兩角和與差的正弦、余弦和正切公式①兩角和與差的正弦公式SKIPIF1<0SKIPIF1<0②兩角和與差的余弦公式SKIPIF1<0SKIPIF1<0③兩角和與差的正切公式SKIPIF1<0SKIPIF1<02、二倍角公式①SKIPIF1<0②SKIPIF1<0；SKIPIF1<0；SKIPIF1<0③SKIPIF1<03、降冪公式SKIPIF1<0SKIPIF1<04、輔助角公式：SKIPIF1<0(其中SKIPIF1<0)5、常用結(jié)論①兩角和與差的正切公式的變形：SKIPIF1<0②SKIPIF1<0③SKIPIF1<0④SKIPIF1<0第二部分：課前自我評估測試第二部分：課前自我評估測試一、判斷題1．（2021·江西·貴溪市實(shí)驗(yàn)中學(xué)高三階段練習(xí)）SKIPIF1<0.()2．（2021·江西·貴溪市實(shí)驗(yàn)中學(xué)高三階段練習(xí)）SKIPIF1<0.()二、單選題3．（2022·北京·高三學(xué)業(yè)考試）SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·四川成都·高一期中（理））SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空題5．（2022·云南玉溪·高一期末）SKIPIF1<0的值等于____________．6．（2022·上海市青浦高級中學(xué)高一階段練習(xí)）將SKIPIF1<0化為SKIPIF1<0的形式為______．第三部分：典型例題剖析第三部分：典型例題剖析高頻考點(diǎn)一：公式的基本應(yīng)用例題1．（2022·江蘇徐州·高一期中）已知SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例題2．（2022·四川成都·高一期中（理））若SKIPIF1<0，SKIPIF1<0是方程SKIPIF1<0兩個實(shí)數(shù)根，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題3．（2022·浙江金華第一中學(xué)高一階段練習(xí)）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題4．（2022·江蘇·淮陰中學(xué)高一階段練習(xí)）求值SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題5．（2022·陜西·榆林市第一中學(xué)高一期中（文））化簡計(jì)算：SKIPIF1<0___________．例題6．（2022·北京·北師大實(shí)驗(yàn)中學(xué)高一期中）若SKIPIF1<0，則SKIPIF1<0___________；SKIPIF1<0___________．題型歸類練1．（2022·河北·滄縣中學(xué)高一階段練習(xí)）SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．－SKIPIF1<0 D．－SKIPIF1<02．（2022·北京市第二十五中學(xué)高一期中）SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·北京·北師大實(shí)驗(yàn)中學(xué)高一期中）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·江蘇·南京外國語學(xué)校高一期中）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·湖南·寧鄉(xiāng)市教育研究中心模擬預(yù)測）若SKIPIF1<0，則SKIPIF1<0=（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·山東德州·高一期中）已知SKIPIF1<0，則SKIPIF1<0______．7．（2022·江蘇·南京師大附中高一期中）設(shè)復(fù)數(shù)SKIPIF1<0，SKIPIF1<0，已知SKIPIF1<0.(1)求SKIPIF1<0的值；(2)若SKIPIF1<0，求SKIPIF1<0的值.高頻考點(diǎn)二：公式的逆用及變形例題1．（2022·江蘇省前黃高級中學(xué)高一階段練習(xí)）SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題2．（2022·江蘇·華羅庚中學(xué)高三階段練習(xí)）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0均為銳角，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題3．（2022·陜西·榆林市第一中學(xué)高一期中（文））SKIPIF1<0___________．例題4．（2022·四川涼山·高一期中（理））SKIPIF1<0_________．例題5．（2022·江蘇·鹽城市伍佑中學(xué)高一期中）求下列各式的值．(1)SKIPIF1<0(2)SKIPIF1<0題型歸類練1．（2022·河南·寶豐縣第一高級中學(xué)模擬預(yù)測（理））SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．SKIPIF1<02．（2022·四川省廣安第三中學(xué)校高一階段練習(xí)）SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<01 D．13．（2022·上海·華東師范大學(xué)附屬天山學(xué)校高一期中）已知SKIPIF1<0，則SKIPIF1<0____________．4．（2022·江蘇·蘇州市蘇州高新區(qū)第一中學(xué)高一期中）化簡：SKIPIF1<0__________．5．（2022·江蘇宿遷·高一期中）在SKIPIF1<0中，已知SKIPIF1<0，則SKIPIF1<0_________6．（2022·江蘇·馬壩高中高一期中）SKIPIF1<0__________.高頻考點(diǎn)三：輔助角公式的運(yùn)用例題1．（2022·全國·高一課時練習(xí)）求下列函數(shù)的最大值和最小值：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<0.例題2．（2021·全國·高一課時練習(xí)）設(shè)m為實(shí)數(shù)，已知SKIPIF1<0，求m的取值范圍．例題3．（2022·黑龍江·勃利縣高級中學(xué)高一階段練習(xí)）求函數(shù)SKIPIF1<0的值域.題型歸類練1．（2022·江西九江·三模（文））已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·江西·南昌市實(shí)驗(yàn)中學(xué)一模（文））SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·湖南·模擬預(yù)測）SKIPIF1<0___________．4．（2022·陜西漢中·高一期中）（1）若SKIPIF1<0，求SKIPIF1<0的值；（2）若SKIPIF1<0，求SKIPIF1<0的值．5．（2021·全國·高一課時練習(xí)）求下列函數(shù)的最大值和最小值：(1)SKIPIF1<0；(2)SKIPIF1<0（a，b均為正數(shù)）.高頻考點(diǎn)四：二倍角例題1．（2022·北京·匯文中學(xué)高一期中）若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題2．（2022·甘肅·永昌縣第一高級中學(xué)高二期中（文））已知SKIPIF1<0，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題3．（2022·全國·高三階段練習(xí)（理））已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題4．（2022·云南曲靖·二模（文））已知SKIPIF1<0，則SKIPIF1<0___________.例題5．（2022·北京·中關(guān)村中學(xué)高一期中）若角SKIPIF1<0的終邊經(jīng)過點(diǎn)SKIPIF1<0，則SKIPIF1<0___________.SKIPIF1<0___________.題型歸類練1．（2022·江西鷹潭·二模（文））已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022·陜西·長安一中模擬預(yù)測（理））已知函數(shù)SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·云南德宏·高三期末（文））已知SKIPIF1<0，則SKIPIF1<0=（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·四川省廣漢中學(xué)高一階段練習(xí)（理））若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·江蘇南通·高一階段練習(xí)）已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·陜西·長安一中高一期中）已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0________．7．（2022·北京市西城外國語學(xué)校高一期中）已知角SKIPIF1<0的終邊在直線SKIPIF1<0上，則SKIPIF1<0________．8．（2022·遼寧沈陽·高一期中）若SKIPIF1<0，則SKIPIF1<0___________.9．（2022·浙江紹興·模擬預(yù)測）已知SKIPIF1<0，則SKIPIF1<0________，SKIPIF1<0__________．高頻考點(diǎn)五：拼湊角例題1．（2022·江蘇·東?？h教育局教研室高一期中）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題2．（2022·江蘇·蘇州市蘇州高新區(qū)第一中學(xué)高一期中）設(shè)SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題3．（2022·江蘇·星海實(shí)驗(yàn)中學(xué)高一期中）已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例題4．（2022·江蘇·漣水縣第一中學(xué)高一階段練習(xí)）已知SKIPIF1<0都是銳角，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型歸類練1．（2022·北京市第五十中學(xué)高一期中）若SKIPIF1<0都是銳角，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·安徽淮南·二模（理））已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．0或SKIPIF1<03．（2022·甘肅省民樂縣第一中學(xué)高一期中）若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·四川成都·高一期中（理））已知SKIPIF1<0、SKIPIF1<0為銳角，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·江蘇省鎮(zhèn)江中學(xué)高一期中）已知SKIPIF1<0為銳角，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．SKIPIF1<0第四部分：高考真題感悟第四部分：高考真題感悟1．（2021·全國·高考真題（文））函數(shù)SKIPIF1<0的最小正周期和最大值分別是（

）A．SKIPIF1<0和SKIPIF1<0 B．SKIPIF1<0和2 C．SKIPIF1<0和SKIPIF1<0 D．SKIPIF1<0和22．（2020·全國·高考真題（理））已知2tanθ–tan(θ+SKIPIF1<0)=7，則tanθ=（

）A．–2 B．–1 C．1 D．23．（2020·全國·高考真題（文））已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2020·全國·高考真題（文））若SKIPIF1<0，則SKIPIF1<0__________．5．（2020·江蘇·高考真題）已知SKIPIF1<0=SKIPIF1<0，則SKIPIF1<0的值是____.6．（2020·浙江·高考真題）已知SKIPIF1<0，則SKIPIF1<0________；SKIPIF1<0______．7．（2021·浙江·高考真題）設(shè)函數(shù)SKIPIF1<0.（1）求函數(shù)SKIPIF1<0的最小正周期；（2）求函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值.第五部分：第03講兩角和與差的正弦、余弦和正切公式（精練）第五部分：第03講兩角和與差的正弦、余弦和正切公式（精練）一、單選題1．（2022·四川省南充市白塔中學(xué)高一期中（文））SKIPIF1<0的值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·江蘇淮安·高一期中）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．－SKIPIF1<0 C．－SKIPIF1<0 D．SKIPIF1<03．（2022·四川涼山·高一期中（理））已知SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·湖南·岳陽市教育科學(xué)技術(shù)研究院三模）SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·四川涼山·高一期中（理））求SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·江蘇·南京市金陵中學(xué)河西分校高一期中）已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·廣東茂名·模擬預(yù)測）已知SKIPIF1<0