我想要问一道关于三角函数的题,希望能尽快解答
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/20 03:58:38
我想要问一道关于三角函数的题,希望能尽快解答
Cos20°+ Cos 60°+ Cos100°+ Cos140°=?
Cos20°+ Cos 60°+ Cos100°+ Cos140°=?
![我想要问一道关于三角函数的题,希望能尽快解答](/uploads/image/z/3985557-69-7.jpg?t=%E6%88%91%E6%83%B3%E8%A6%81%E9%97%AE%E4%B8%80%E9%81%93%E5%85%B3%E4%BA%8E%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E7%9A%84%E9%A2%98%2C%E5%B8%8C%E6%9C%9B%E8%83%BD%E5%B0%BD%E5%BF%AB%E8%A7%A3%E7%AD%94)
Cos20°+ Cos 60°+ Cos100°+ Cos140°
=(Cos20°+Cos140°)+(Cos60°+Cos100°)
=2Cos80°Cos60° + 2Cos80°Cos20°
=2Cos80°(Cos60°+Cos20°)
=4Cos80°Cos40°Cos20°
=(4Cos80°Cos40°Cos20°Sin20 °)/Sin20°
=0.5
=(Cos20°+Cos140°)+(Cos60°+Cos100°)
=2Cos80°Cos60° + 2Cos80°Cos20°
=2Cos80°(Cos60°+Cos20°)
=4Cos80°Cos40°Cos20°
=(4Cos80°Cos40°Cos20°Sin20 °)/Sin20°
=0.5