计算:(sin20°-sin40°)÷(cos20°-cos40°),答案是-根号3,求详解!急急急急急!

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（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

(sin20-sin40)÷(cos20-cos40)
= [ sin(30-10)-sin(30+10) ] ÷ [ cos(30-10)-cos(30+10) ]
= (-2cos30sin10)÷(2sin30sin10)
= -cot30
= -√3