sin50°(1+根号3tan10°)

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 23:15:28
sin50°(1+根号3tan10°)

sin50°(1+根号3tan10°)
sin50°(1+根号3tan10°)

sin50°(1+根号3tan10°)
=sin50°(1+根号3sin10°/cos10°)
=sin50° * 2 * (cos10°/2+根号3sin10°/2)/cos10°通分后括号内提出2
=2sin50°sin(10°+30°)/cos10°诱导公式
=2sin50°cos(90°-40°)/cos10°诱导公式sin cos 转换
=sin100°/cos10°
=cos10°/cos10°
=1

sin50(1+√3tan10)
=sin50[1+√3(sin10/cos10)]
=sin50[(cos10+√3sin10)/cos10]
=sin50[2sin(30+10)/cos10]
=(2sin50sin40)/cos10°
=(2cos40°*sin40°)/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1