Question

（tan10°－√3）×cos10°÷sin50°=?

Answer 1

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

Answer 2

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

Answer 3

用计算机算不就完了

Answer 4

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