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

问题描述:

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

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