（cos20°-cos40°)/(sin20°-sin40°）=[cos(30°-10°)-cos(30°+10°)]/[sin(30°-10°)-sin(30°+10°)] =[(cos30°cos10°+sin30°sin10°)-(cos30°cos10°-sin30°sin10°)]/[(sin30°cos10°-cos30°sin10°)-(sin30°cos10°-cos30°sin10°)]=（2sin30sin10°)/（-2cos30sin10°)=-tan30°=-√3/3
采纳哦