新高考数学二轮复习考点讲义第十二讲三角恒等变换（原卷版）

第十二讲：简单的三角恒等变换【考点梳理】两角和与差的三角函数公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0二倍角公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<03、辅助角公式SKIPIF1<0(其中SKIPIF1<0)4、降幂公式SKIPIF1<0SKIPIF1<0【典型题型讲解】考点一：两角和与差公式【典例例题】例1．（2022·广东汕头·高三期末）已知SKIPIF1<0，则SKIPIF1<0（

）A．-1 B．0 C．SKIPIF1<0 D．SKIPIF1<0例2.（2022·广东湛江·一模）已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例3．（2022·广东汕头·一模）已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．SKIPIF1<0【方法技巧与总结】1.三角函数式化简的方法：化简三角函数式常见方法有弦切互化，异名化同名，异角化同角，降幂与升幂等.2.给值求值：解题的关键在于“变角”，把待求三角函数值的角用含已知角的式子表示出来，求解时要注意对角的范围的讨论.【变式训练】1.已知SKIPIF1<0，则SKIPIF1<0__________．2.（2022·广东韶关·一模）若SKIPIF1<0，则SKIPIF1<0__________.3.（2022·全国·高考真题）若SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04.已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05.已知SKIPIF1<0，则SKIPIF1<0的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点二：二倍角公式【典例例题】例1.（2022·广东中山·高三期末）若SKIPIF1<0，则SKIPIF1<0___________.例2．（2022·广东清远·高三期末）已知SKIPIF1<0，则SKIPIF1<0________．例3.若SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【方法技巧与总结】三角恒等变换的基本思路：找差异，化同角(名)，化简求值.三角恒等变换的关键在于观察各个角之间的联系，发现题目所给条件与恒等变换公式的联系.【变式训练】1．（2022·广东汕头·一模）已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．SKIPIF1<02．（2022·广东韶关·二模）已知SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03.（2022·广东佛山·二模）已知sinSKIPIF1<0，则SKIPIF1<0___________.4.（2022·广东肇庆·二模）若SKIPIF1<0，则SKIPIF1<0______．5．（2022·广东深圳·二模）已知SKIPIF1<0，则SKIPIF1<0__________．6.若SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．27．已知SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【巩固练习】一、单选题1．已知角SKIPIF1<0与角SKIPIF1<0的顶点均与原点O重合，始边均与x轴的非负半轴重合，它们的终边关于x轴对称．若SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．0 B．SKIPIF1<0 C．SKIPIF1<0 D．13．已知SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．2或64．公元前6世纪，古希腊的毕达哥拉斯学派研究过正五边形和正十边形的作图，发现了黄金分割约为0.618，这一数值也可以表示为SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0（

）A．－4 B．－2 C．2 D．45．若SKIPIF1<0，则SKIPIF1<0的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．若SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多选题7．已知SKIPIF1<0，SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．下列各式的值为SKIPIF1<0的是（

）.A．sinSKIPIF1<0B．sinSKIPIF1<0cosSKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知SKIPIF1<0，其中SKIPIF1<0为锐角，则以下命题正确的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空题10．若SKIPIF1<0，则SKIPIF1<0__________，SKIPIF1<0_________．11．已知SKIPIF1<0，则SKIPIF1<0________.12．已知SKIPIF1<0，则SKIPIF1<0_____________.13．SKIPIF1<0__________.四、解答题14．已知SKIPIF1<0，SKIPIF1<0．(1)求SKIPIF1<0的值；(2)若SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的值．15．已知角SKIPIF1<0为锐角，SKIPIF1<0