化简sin50(1+√3tan10)

来源:学生作业学帮网 编辑:学帮网 时间:2024/05/15 09:31:30

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