cos15°-sin15°=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/07 20:53:11

cos15°-sin15°=?
cos15°-sin15°=?

cos15°-sin15°=?
cos15°-sin15°
= cos(45°- 30°) - sin(45°- 30°)
= cos45°cos30°+ sin45°sin30°- sin45°cos30°+ cos45°sin30°
= √2/2 * cos30°+ √2/2 * sin30°- √2/2 * cos30°+ √2/2 * sin30°
= √2/2 * ( cos30°+ sin30°- cos30°+ sin30°)
= √2/2 * ( 2 * sin30°)
= √2/2 * ( 2 * 1/2)
= √2/2

cos15°-sin15°=cos(45°-30°)-sin(45°-30°)
=cos45°cos30°+sin45°sin30°-sin45°cos30°+cos45°sin30°
=√2/2*√3/2+√2/2*1/2-√2/2*√3/2+√2/2*1/2=√2/2.

cos15°-sin15°=cos(15°+15°)=cos30°=√3/2