用两角的和差公式求值 1.cos²105°-sin²105° 2.sin20°sin10°-cos10°sin70°3.½cosα+√3/2 sinα 4.√2cosα-√2sinα 5.sinα+cosα 6.sin200°sin310°+cos340°cos50°
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 14:12:19
![用两角的和差公式求值 1.cos²105°-sin²105° 2.sin20°sin10°-cos10°sin70°3.½cosα+√3/2 sinα 4.√2cosα-√2sinα 5.sinα+cosα 6.sin200°sin310°+cos340°cos50°](/uploads/image/z/15211943-71-3.jpg?t=%E7%94%A8%E4%B8%A4%E8%A7%92%E7%9A%84%E5%92%8C%E5%B7%AE%E5%85%AC%E5%BC%8F%E6%B1%82%E5%80%BC+1.cos%26sup2%3B105%C2%B0-sin%26sup2%3B105%C2%B0+2.sin20%C2%B0sin10%C2%B0-cos10%C2%B0sin70%C2%B03.%26frac12%3Bcos%CE%B1%2B%E2%88%9A3%2F2+sin%CE%B1+4.%E2%88%9A2cos%CE%B1-%E2%88%9A2sin%CE%B1+5.sin%CE%B1%2Bcos%CE%B1+6.sin200%C2%B0sin310%C2%B0%2Bcos340%C2%B0cos50%C2%B0)
用两角的和差公式求值 1.cos²105°-sin²105° 2.sin20°sin10°-cos10°sin70°3.½cosα+√3/2 sinα 4.√2cosα-√2sinα 5.sinα+cosα 6.sin200°sin310°+cos340°cos50°
用两角的和差公式求值
1.cos²105°-sin²105° 2.sin20°sin10°-cos10°sin70°3.½cosα+√3/2 sinα 4.√2cosα-√2sinα 5.sinα+cosα 6.sin200°sin310°+cos340°cos50°
用两角的和差公式求值 1.cos²105°-sin²105° 2.sin20°sin10°-cos10°sin70°3.½cosα+√3/2 sinα 4.√2cosα-√2sinα 5.sinα+cosα 6.sin200°sin310°+cos340°cos50°
1.cos²105°-sin²105°=cos(2×105°) =cos(210°)=-cos30°=-√3/2
2.sin20°sin10°-cos10°sin70°=cos70°sin10°-cos10°sin70°=sin(10°-70°)=-sin60°=-√3/2
3.½cosα+√3/2 sinα =sin30°cosα+cos30°sinα=sin(α+30°)
4.√2cosα-√2sinα =1/2(√2/2cosα-√2/2sinα )=1/2(sin45°cosα-cos45°sinα )=1/2sin(45°-α)
5.sinα+cosα =√2(√2/2sinα+√2/2cosα )=√2(cos45°sinα +sin45°cosα)=√2sin(α+45°)
6.sin200°sin310°+cos340°cos50°
=sin(-20°)sin(-50°)+cos20°cos50°
=sin20°sin50°+cos20°cos50°
=cos20°cos50°+sin20°sin50°
=cos(20°-50°)
=cos(-30°)
=cos30°
=√3/2