(tan10°-√3)×cos10°÷sin50°=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 01:29:26
(tan10°-√3)×cos10°÷sin50°=?

(tan10°-√3)×cos10°÷sin50°=?
(tan10°-√3)×cos10°÷sin50°=?

(tan10°-√3)×cos10°÷sin50°=?
tan10°-√3=tan10°-tan60°
利用公式tanα-tanβ=sin(α-β)/(cosα·cosβ)得
tan10°-tan60°=-sin50°/(cos10°cos60°)
(tan10°-√3)×cos10°÷sin50°
=(tan10°-tan60°)cos10°/sin50°
=[-sin50°/(cos10°cos60°)]cos10°/sin50°
=-1/cos60°
=-2

=[sin10°/cos10°-√3]cos10°/sin50°
=[sin10°-√3cos10°]/sin50°
=2[sin10°cos60°-cos10°sin60°]/sin50°
=2sin(10°-60°)/sin50°
=-2

用计算机算不就完了

(tan10°-√3)×cos10°÷sin50°=(sin10°-√3×cos10°)÷sin50°
=2×(sin10°/2-√3×cos10°/2)÷sin50°=-2×sin50°÷sin50°=-2