(cos10度-sin40度)除以(sin10度-cos40度)=?

题目

(cos10度-sin40度)除以(sin10度-cos40度)=?

答案

(cos10°-sin40°)/(sin10°-cos40°)
=(cos10°-sin(30°+10°))/(sin10°-cos(30°+10°))
=(cos10°-sin30°cos10°- cos30°sin10°))/(sin10°- cos30°cos10°+sin30°sin10°)
=(1/2 cos10°- cos30°sin10°))/（3/2 sin10°- cos30°cos10°）
= (sin30°cos10°- cos30°sin10°))/[ √3 (√3/2 sin10°-1/2cos10°)]
= sin(30°-10°)/ [ √3sin(10°-30°)]
=-√3/3.