已知锐角三角形ABC的对边分别是abc,∠A=60°,求sin(A+10°)*【1-根号3tan(A-10°)】的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 12:38:28
![已知锐角三角形ABC的对边分别是abc,∠A=60°,求sin(A+10°)*【1-根号3tan(A-10°)】的值](/uploads/image/z/11373232-40-2.jpg?t=%E5%B7%B2%E7%9F%A5%E9%94%90%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E5%AF%B9%E8%BE%B9%E5%88%86%E5%88%AB%E6%98%AFabc%2C%E2%88%A0A%3D60%C2%B0%2C%E6%B1%82sin%EF%BC%88A%2B10%C2%B0%EF%BC%89%2A%E3%80%901-%E6%A0%B9%E5%8F%B73tan%EF%BC%88A-10%C2%B0%EF%BC%89%E3%80%91%E7%9A%84%E5%80%BC)
已知锐角三角形ABC的对边分别是abc,∠A=60°,求sin(A+10°)*【1-根号3tan(A-10°)】的值
已知锐角三角形ABC的对边分别是abc,∠A=60°,求sin(A+10°)*【1-根号3tan(A-10°)】的值
已知锐角三角形ABC的对边分别是abc,∠A=60°,求sin(A+10°)*【1-根号3tan(A-10°)】的值
sin(A+10°)*【1-根号3tan(A-10°)】
=sin(60°+10°)*[1-√3tan(60°-10°)]
=sin70°*[1-√3tan50°
=2sin70°*[(1/2)cos50°-(√3/2)sin50°]/cos50°
=2sin70°sin(30°-50°)/sin40°
=-2sin20°cos20°/sin40°
=-sin40°/sin40°
=-1
希望能帮到你,祝学习进步O(∩_∩)O