sin50°(1+√3tan10°)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 04:23:44
sin50°(1+√3tan10°)=?

sin50°(1+√3tan10°)=?
sin50°(1+√3tan10°)=?

sin50°(1+√3tan10°)=?
1+√3tan10
=1+√3sin10/cos10
=(cos10+√3sin10)/cos10
=2sin(10+30)/cos10
=2sin40/cos10
sin50(1+√3tan10)
=(2sin40sin50)/cos10
=[cos(50-40)-cos(50+40)]/cos10
=cos10/cos10
=1

sin50(1+√3tan10)
=2sin50[(1/2)+[ (√3/2)(sin10/cos10)]
=2sin50[sin30+cos30(sin10/cos10)]
=2sin50/cos10[sin30cos10+cos30sin10]
=2sin50/cos10*sin40
=(2cos40sin40)/cos10
=sin80/cos10
=cos10/cos10
=1