新高考數(shù)學(xué)二輪復(fù)習(xí)考點講義第十二講三角恒等變換（原卷版）

第十二講：簡單的三角恒等變換【考點梳理】兩角和與差的三角函數(shù)公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0二倍角公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<03、輔助角公式SKIPIF1<0(其中SKIPIF1<0)4、降冪公式SKIPIF1<0SKIPIF1<0【典型題型講解】考點一：兩角和與差公式【典例例題】例1．（2022·廣東汕頭·高三期末）已知SKIPIF1<0，則SKIPIF1<0（

）A．-1 B．0 C．SKIPIF1<0 D．SKIPIF1<0例2.（2022·廣東湛江·一模）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例3．（2022·廣東汕頭·一模）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．SKIPIF1<0【方法技巧與總結(jié)】1.三角函數(shù)式化簡的方法：化簡三角函數(shù)式常見方法有弦切互化，異名化同名，異角化同角，降冪與升冪等.2.給值求值：解題的關(guān)鍵在于“變角”，把待求三角函數(shù)值的角用含已知角的式子表示出來，求解時要注意對角的范圍的討論.【變式訓(xùn)練】1.已知SKIPIF1<0，則SKIPIF1<0__________．2.（2022·廣東韶關(guān)·一模）若SKIPIF1<0，則SKIPIF1<0__________.3.（2022·全國·高考真題）若SKIPIF1<0，則（

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

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05.已知SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點二：二倍角公式【典例例題】例1.（2022·廣東中山·高三期末）若SKIPIF1<0，則SKIPIF1<0___________.例2．（2022·廣東清遠(yuǎn)·高三期末）已知SKIPIF1<0，則SKIPIF1<0________．例3.若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【方法技巧與總結(jié)】三角恒等變換的基本思路：找差異，化同角(名)，化簡求值.三角恒等變換的關(guān)鍵在于觀察各個角之間的聯(lián)系，發(fā)現(xiàn)題目所給條件與恒等變換公式的聯(lián)系.【變式訓(xùn)練】1．（2022·廣東汕頭·一模）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．SKIPIF1<02．（2022·廣東韶關(guān)·二模）已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03.（2022·廣東佛山·二模）已知sinSKIPIF1<0，則SKIPIF1<0___________.4.（2022·廣東肇慶·二模）若SKIPIF1<0，則SKIPIF1<0______．5．（2022·廣東深圳·二模）已知SKIPIF1<0，則SKIPIF1<0__________．6.若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

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

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

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

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

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【鞏固練習(xí)】一、單選題1．已知角SKIPIF1<0與角SKIPIF1<0的頂點均與原點O重合，始邊均與x軸的非負(fù)半軸重合，它們的終邊關(guān)于x軸對稱．若SKIPIF1<0，則SKIPIF1<0（

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

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

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．2或64．公元前6世紀(jì)，古希臘的畢達(dá)哥拉斯學(xué)派研究過正五邊形和正十邊形的作圖，發(fā)現(xiàn)了黃金分割約為0.618，這一數(shù)值也可以表示為SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

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

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

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題7．已知SKIPIF1<0，SKIPIF1<0，則（

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

）.A．sinSKIPIF1<0B．sinSKIPIF1<0cosSKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知SKIPIF1<0，其中SKIPIF1<0為銳角，則以下命題正確的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空題10．若SKIPIF1<0，則SKIPIF1<0__________，SKIPIF1<0_________．11．已知SKIPIF1<0，則SKIPIF1<0________.12．已知SKIPIF1<0，則SKIPIF1<0_____________.13．SKIPIF1<0__________.四、解答題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為銳角，SKIPIF1<0