化简sin50(1+√3tan10)

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/14 14:44:43

化简sin50(1+√3tan10)
化简sin50(1+√3tan10)

化简sin50(1+√3tan10)
sin50°(1+√3tan10°)
=sin50°(1+√3sin10°/cos10°)
=sin50°(cos10°+√3sin10°)/cos10°
=2sin50°sin(30°+10°)/cos10°
=2sin50°sin40°/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1

sin50°(1+√3sin10°/cos10°)=sin50°(cos10°+√3sin10°)/cos10°=2sin50°sin(30°+10°)/cos10°=2sin50°sin40°/cos10°=2cos40°sin40°/cos10°=sin80°/cos10°cos10°/cos10°
=1