新高考数学一轮复习第4章 第03讲 两角和与差的正弦、余弦和正切公式 精讲+精练（学生版）

第03讲两角和与差的正弦、余弦和正切公式(精讲+精练）目录第一部分：知识点精准记忆第二部分：课前自我评估测试第三部分：典型例题剖析高频考点一：公式的基本应用高频考点二：公式的逆用及变形高频考点三：辅助角公式的运用高频考点四：二倍角高频考点五：拼凑角第四部分：高考真题感悟第五部分：第03讲两角和与差的正弦、余弦和正切公式（精练）第一部分：知识点精准记忆第一部分：知识点精准记忆1、两角和与差的正弦、余弦和正切公式①两角和与差的正弦公式SKIPIF1<0SKIPIF1<0②两角和与差的余弦公式SKIPIF1<0SKIPIF1<0③两角和与差的正切公式SKIPIF1<0SKIPIF1<02、二倍角公式①SKIPIF1<0②SKIPIF1<0；SKIPIF1<0；SKIPIF1<0③SKIPIF1<03、降幂公式SKIPIF1<0SKIPIF1<04、辅助角公式：SKIPIF1<0(其中SKIPIF1<0)5、常用结论①两角和与差的正切公式的变形：SKIPIF1<0②SKIPIF1<0③SKIPIF1<0④SKIPIF1<0第二部分：课前自我评估测试第二部分：课前自我评估测试一、判断题1．（2021·江西·贵溪市实验中学高三阶段练习）SKIPIF1<0.()2．（2021·江西·贵溪市实验中学高三阶段练习）SKIPIF1<0.()二、单选题3．（2022·北京·高三学业考试）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、填空题5．（2022·云南玉溪·高一期末）SKIPIF1<0的值等于____________．6．（2022·上海市青浦高级中学高一阶段练习）将SKIPIF1<0化为SKIPIF1<0的形式为______．第三部分：典型例题剖析第三部分：典型例题剖析高频考点一：公式的基本应用例题1．（2022·江苏徐州·高一期中）已知SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例题2．（2022·四川成都·高一期中（理））若SKIPIF1<0，SKIPIF1<0是方程SKIPIF1<0两个实数根，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题3．（2022·浙江金华第一中学高一阶段练习）已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题4．（2022·江苏·淮阴中学高一阶段练习）求值SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题5．（2022·陕西·榆林市第一中学高一期中（文））化简计算：SKIPIF1<0___________．例题6．（2022·北京·北师大实验中学高一期中）若SKIPIF1<0，则SKIPIF1<0___________；SKIPIF1<0___________．题型归类练1．（2022·河北·沧县中学高一阶段练习）SKIPIF1<0（

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

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·北京·北师大实验中学高一期中）已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·江苏·南京外国语学校高一期中）已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·湖南·宁乡市教育研究中心模拟预测）若SKIPIF1<0，则SKIPIF1<0=（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·山东德州·高一期中）已知SKIPIF1<0，则SKIPIF1<0______．7．（2022·江苏·南京师大附中高一期中）设复数SKIPIF1<0，SKIPIF1<0，已知SKIPIF1<0.(1)求SKIPIF1<0的值；(2)若SKIPIF1<0，求SKIPIF1<0的值.高频考点二：公式的逆用及变形例题1．（2022·江苏省前黄高级中学高一阶段练习）SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题2．（2022·江苏·华罗庚中学高三阶段练习）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0均为锐角，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题3．（2022·陕西·榆林市第一中学高一期中（文））SKIPIF1<0___________．例题4．（2022·四川凉山·高一期中（理））SKIPIF1<0_________．例题5．（2022·江苏·盐城市伍佑中学高一期中）求下列各式的值．(1)SKIPIF1<0(2)SKIPIF1<0题型归类练1．（2022·河南·宝丰县第一高级中学模拟预测（理））SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．SKIPIF1<02．（2022·四川省广安第三中学校高一阶段练习）SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<01 D．13．（2022·上海·华东师范大学附属天山学校高一期中）已知SKIPIF1<0，则SKIPIF1<0____________．4．（2022·江苏·苏州市苏州高新区第一中学高一期中）化简：SKIPIF1<0__________．5．（2022·江苏宿迁·高一期中）在SKIPIF1<0中，已知SKIPIF1<0，则SKIPIF1<0_________6．（2022·江苏·马坝高中高一期中）SKIPIF1<0__________.高频考点三：辅助角公式的运用例题1．（2022·全国·高一课时练习）求下列函数的最大值和最小值：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<0.例题2．（2021·全国·高一课时练习）设m为实数，已知SKIPIF1<0，求m的取值范围．例题3．（2022·黑龙江·勃利县高级中学高一阶段练习）求函数SKIPIF1<0的值域.题型归类练1．（2022·江西九江·三模（文））已知SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·江西·南昌市实验中学一模（文））SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·湖南·模拟预测）SKIPIF1<0___________．4．（2022·陕西汉中·高一期中）（1）若SKIPIF1<0，求SKIPIF1<0的值；（2）若SKIPIF1<0，求SKIPIF1<0的值．5．（2021·全国·高一课时练习）求下列函数的最大值和最小值：(1)SKIPIF1<0；(2)SKIPIF1<0（a，b均为正数）.高频考点四：二倍角例题1．（2022·北京·汇文中学高一期中）若SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题2．（2022·甘肃·永昌县第一高级中学高二期中（文））已知SKIPIF1<0，则SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题3．（2022·全国·高三阶段练习（理））已知SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题4．（2022·云南曲靖·二模（文））已知SKIPIF1<0，则SKIPIF1<0___________.例题5．（2022·北京·中关村中学高一期中）若角SKIPIF1<0的终边经过点SKIPIF1<0，则SKIPIF1<0___________.SKIPIF1<0___________.题型归类练1．（2022·江西鹰潭·二模（文））已知SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022·陕西·长安一中模拟预测（理））已知函数SKIPIF1<0，则SKIPIF1<0的最小值为（

）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，则SKIPIF1<0=（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·四川省广汉中学高一阶段练习（理））若SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·江苏南通·高一阶段练习）已知SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·陕西·长安一中高一期中）已知SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0________．7．（2022·北京市西城外国语学校高一期中）已知角SKIPIF1<0的终边在直线SKIPIF1<0上，则SKIPIF1<0________．8．（2022·辽宁沈阳·高一期中）若SKIPIF1<0，则SKIPIF1<0___________.9．（2022·浙江绍兴·模拟预测）已知SKIPIF1<0，则SKIPIF1<0________，SKIPIF1<0__________．高频考点五：拼凑角例题1．（2022·江苏·东海县教育局教研室高一期中）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题2．（2022·江苏·苏州市苏州高新区第一中学高一期中）设SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题3．（2022·江苏·星海实验中学高一期中）已知SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题4．（2022·江苏·涟水县第一中学高一阶段练习）已知SKIPIF1<0都是锐角，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0题型归类练1．（2022·北京市第五十中学高一期中）若SKIPIF1<0都是锐角，且SKIPIF1<0，SKIPIF1<0，则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，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．0或SKIPIF1<03．（2022·甘肃省民乐县第一中学高一期中）若SKIPIF1<0，SKIPIF1<0，则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为锐角，且SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·江苏省镇江中学高一期中）已知SKIPIF1<0为锐角，SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．SKIPIF1<0第四部分：高考真题感悟第四部分：高考真题感悟1．（2021·全国·高考真题（文））函数SKIPIF1<0的最小正周期和最大值分别是（

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

）A．–2 B．–1 C．1 D．23．（2020·全国·高考真题（文））已知SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2020·全国·高考真题（文））若SKIPIF1<0，则SKIPIF1<0__________．5．（2020·江苏·高考真题）已知SKIPIF1<0=SKIPIF1<0，则SKIPIF1<0的值是____.6．（2020·浙江·高考真题）已知SKIPIF1<0，则SKIPIF1<0________；SKIPIF1<0______．7．（2021·浙江·高考真题）设函数SKIPIF1<0.（1）求函数SKIPIF1<0的最小正周期；（2）求函数SKIPIF1<0在SKIPIF1<0上的最大值.第五部分：第03讲两角和与差的正弦、余弦和正切公式（精练）第五部分：第03讲两角和与差的正弦、余弦和正切公式（精练）一、单选题1．（2022·四川省南充市白塔中学高一期中（文））SKIPIF1<0的值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·江苏淮安·高一期中）已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．－SKIPIF1<0 C．－SKIPIF1<0 D．SKIPIF1<03．（2022·四川凉山·高一期中（理））已知SKIPIF1<0，则SKIPIF1<0的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·湖南·岳阳市教育科学技术研究院三模）SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·四川凉山·高一期中（理））求SKIPIF1<0的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·江苏·南京市金陵中学河西分校高一期中）已知SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·广东茂名·模拟预测）已知SKIPIF1<0