简单三角恒等变换复习
一、公式体系
1、和差公式及其变形：
（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"231f2f1850be1e73bc1242f210026d6e.png"})
（2）![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"57f703a9795f1cb4d17ff39b993fe18b.png"})
（3）![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"2d70bb770b622c114d8ff7f9f94ab34c.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"c8460ca63880b5f03bcb9a856337c9a8.png"})
2、倍角公式的推导及其变形：
（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"08f3d9342a62490eca01e14401132f1c.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"ce357ab6ce19991b864bf7e6a01b9da7.png"})
（2）![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"1e57c9fb6b585aa1da868e399f46bc55.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"653972348c63e7f08b8657e92945e939.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"5ae3e386f94a4d0e35e439ddbd68910c.png"})
【因为![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"ab410a966ac148e9b78c65c6cdf301fd.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"2663947996ef999af3215bc19771aedd.png"})
因为![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"7ed59bad51e1d241073a885d429a9a6a.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"49d664c49efdb39ae2b61173310a753d.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"2772b309c290112f6bb133d588287424.png"})
【因为
![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"7489c4f849847538a9d16faa56bea0d9.png"})
因为
![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"28681b5e719160bd5efce95f6555d1a4.png"})
二、基本题型
1、已知某个三角函数，求其他的三角函数：
注意角的关系，如![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"7742b49a8652e5f995b2e73c82eb0b96.png"})
（1）已知![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"5f2abeeac98cd1096d5658f9f306e651.png"})
（2）已知![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"56bc422c939ed95290292c14f191461d.png"})
（提示：![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"1b847147a23970bb371615770052b3a6.png"})
2、已知某个三角函数值，求相应的角：只要计算所求角的某个三角函数，再由三角函数值求角，注意选择合适的三角函数
（1）已知
3、![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"5e731757d6fe81bb0285c5ae5cd18995.png"})
（1）求![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"e727d8421c823a3b83b262af5edf43a1.png"})
（2）△ABC中，角A、B满足![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"72fad8fdd21eebbc198762e67f194e6c.png"})
4、弦化切，即已知tan，求与sin，cos相关的式子的值：化为分式，分子分母同时除以![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"2c41d5ac43d502c2e4590d5e4e039630.png"})
（1）已知![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"1f5733043cfc3a4f98cee9cd89c693e3.png"})
5、切化弦，再通分，再弦合一
（1）、化简：① ![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"3a11bd7012a8d28f717d72e9c47c3113.png"})
（2）、证明：![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"362c42972db48da3f70af8959b415cc2.png"})
6、综合应用，注意公式的灵活应用与因式分解结合
化简![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"7599b025d7bf29be6127c863057ba890.png"})
1、![](https://wkrtcs.bdimg.com/rtcs/image?w=273&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"273","h":"25","c":"865778e99a051f27a8256d2072f244a4.png"})
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"16","h":"43","c":"eca3bf81573307ec3002cf846390d363.png"})
2、若![](https://wkrtcs.bdimg.com/rtcs/image?w=76&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"76","h":"20","c":"1daebfad6b516eacb1ea12cde9e0f6d7.png"})
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=29&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"29","h":"20","c":"1b6b3e808a3cc205dfcbe4e119f59025.png"})
3、cos![](https://wkrtcs.bdimg.com/rtcs/image?w=17&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"17","h":"43","c":"cb7b3df49ac033e9e871de5bacd20ab5.png"})
A．
4、 已知![](https://wkrtcs.bdimg.com/rtcs/image?w=73&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"73","h":"43","c":"d53a9641eae693059a43c0a427d3ce41.png"})
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=27&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"27","h":"43","c":"44e2e534883f6102dc3db1b68586c89b.png"})
5、已知![](https://wkrtcs.bdimg.com/rtcs/image?w=268&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"268","h":"43","c":"e014b7d1fe63a8ea7a34b37a83cd4f81.png"})
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=28&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"28","h":"43","c":"c316946cab6b96fb158f4a54dbddb785.png"})
6、sin165º= （ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"16","h":"43","c":"93b05c90d14a117ba52da1d743a43ab1.png"})
7、sin14ºcos16º+sin76ºcos74º的值是（ ）
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=29&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","w":"29","h":"52","c":"aed430fdf4c64058b58e05bf9ccbbbde.png"})
8、已知![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"7c602a0a470e0f5956a89cf45f763327.png"})
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"74be9009964746fd6030af234932cd9d.png"})
9、化简2sin（![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"cd3ba7dbe6650fbf0b092d3d3c833d5d.png"})
Ａ．sin2x![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"d41d8cd98f00b204e9800998ecf8427e.png"})
10、sin![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"fd2182b876efceaa7332588de22f653f.png"})
A．0 B． —![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"d21848cdd835abcb491be1f151e9b6c6.png"})
11、![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"7041c438b530d34ff5a22f1c77686dec.png"})
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=&md5sum=78041db96702f23d1b371282e6016999&sign=1d6b3f4fc9&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=486&ipr={"t":"img","c":"93e49565abe3ac8e8986a91474d2f5ee.png"})
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