和差倍半角公式的应用
参考答案
1．求word/media/image1.gif．
解：word/media/image2.gif；
word/media/image3.gif；
word/media/image4.gif；
word/media/image5.gif；
word/media/image6.gif；
word/media/image7.gif．
2．word/media/image8.gif，
word/media/image9.gif为第二象限角，求
word/media/image10.gif．
解：由题，word/media/image11.gif．
word/media/image12.gif；
word/media/image13.gif．
3．word/media/image14.gif．求
word/media/image15.gif．
解：由题，word/media/image16.gif．
word/media/image17.gif．
4．设word/media/image18.gif为钝角，且
word/media/image19.gif，求
word/media/image20.gif．
解：由题，word/media/image21.gif．
word/media/image22.gif．
又word/media/image18.gif为钝角，
word/media/image23.gif．
word/media/image24.gif．
5．已知word/media/image25.gif，求
word/media/image26.gif．
解：由题，word/media/image27.gif，则
word/media/image28.gif．
word/media/image29.gif
6．一元二次方程word/media/image30.gif的两根为
word/media/image31.gif，求
word/media/image32.gif的最小值．
解：由题，word/media/image33.gif，得
word/media/image34.gif．
又word/media/image35.gif，
word/media/image36.gif．易知，当
word/media/image37.gif时，
word/media/image38.gif．
7．word/media/image39.gif，
word/media/image9.gif为第二象限角，求
word/media/image40.gif．
解：由题，word/media/image41.gif，则
word/media/image42.gif．那么
word/media/image43.gif；
word/media/image44.gif．
8．已知word/media/image18.gif为锐角，且
word/media/image45.gif，且
word/media/image46.gif．
解：由题，word/media/image47.gif．
而word/media/image48.gif（
word/media/image18.gif为锐角），故
word/media/image49.gif．
word/media/image50.gif．
9．已知word/media/image51.gif，求
word/media/image52.gif．
word/media/image53.gif
10．已知word/media/image54.gif，求
word/media/image55.gif．
word/media/image56.gif
11．已知word/media/image57.gif，求
word/media/image58.gif．
word/media/image59.gif
12．已知word/media/image60.gif，求
word/media/image61.gif与
word/media/image62.gif．
word/media/image63.gif
word/media/image64.gif
13．已知word/media/image65.gif，求
word/media/image66.gif与
word/media/image67.gif．
word/media/image68.gif
word/media/image69.gif
14．已知word/media/image70.gif，求
word/media/image71.gif．
解：word/media/image72.gif．
15．已知word/media/image73.gif，求
word/media/image74.gif．
解：由题word/media/image75.gif．那么
word/media/image76.gif；
word/media/image77.gif；
由word/media/image78.gif，知
word/media/image79.gif，则
word/media/image80.gif．
16．已知word/media/image81.gif，求
word/media/image82.gif．
解：由题word/media/image83.gif，得
word/media/image84.gif，则
word/media/image85.gif．
17．已知word/media/image86.gif，且
word/media/image87.gif，求
（Ⅰ）word/media/image88.gif；
（Ⅱ）word/media/image89.gif．
解：由word/media/image90.gif，得
word/media/image91.gif，或
word/media/image92.gif．
word/media/image93.gif，
word/media/image94.gif．则
word/media/image95.gif．
（Ⅰ）word/media/image96.gif；
（Ⅱ）由题，word/media/image97.gif，则
word/media/image98.gif．那么
word/media/image99.gif，
而word/media/image100.gif，则
word/media/image101.gif，
word/media/image102.gif．
18．化简word/media/image103.gif．
word/media/image104.gif
19．已知word/media/image105.gif，求
word/media/image26.gif．
解：由题，word/media/image106.gif
word/media/image107.gif，得
word/media/image108.gif，即
word/media/image109.gif．
20．化简word/media/image110.gif．
word/media/image111.gif
21．化简word/media/image112.gif．
word/media/image113.gif
22．已知函数word/media/image114.gif．求
（Ⅰ）单调区间与周期；
（Ⅱ）当word/media/image115.gif时，函数的值域．
word/media/image116.gif
（Ⅰ）由word/media/image117.gif，得
word/media/image118.gif，
word/media/image119.gif原函数的单调递增区间为
word/media/image120.gif；
由word/media/image121.gif，得
word/media/image122.gif，
word/media/image119.gif原函数的单调递减区间为
word/media/image123.gif；
原函数的周期为word/media/image124.gif；
（Ⅱ）当word/media/image115.gif时，
word/media/image125.gif，则
word/media/image126.gif．
word/media/image119.gif原函数的值域为
word/media/image127.gif．
本文来源：https://www.2haoxitong.net/k/doc/4f81559a33687e21ae45a9a9.html
文档为doc格式