(2cos40度-cos20度)/sin20度
=(cos40°+cos40°-cos20°)/sin20°
=(cos40°+cos(30°+10°)-cos(30°-10°))/sin20°
=(cos40°-2sin30°sin10°)/sin20°
=(cos40°-sin10°)/sin20°
=(sin50°-sin10°)/sin20°
=(sin(30°+20°)-sin(30°-20°))/sin20°
=2cos30°sin20°/sin20°
=2cos30°
=√3