题目有误吧.如果按你的题目答案不是特殊值,约等于4.11556
应该是 1/sin20°-1/tan40°吧
1/sin 20°-1/tan 40 °
= (2cos20°)/(2sin20°cos20°)-cos40°/sin40°
=(2cos20°-cos40°)/sin40°
=[2cos(60°-40°)-cos40°]/sin40°
=(2cos60°cos40°+2sin60°sin40°-cos40°)/sin40°
=2sin60°sin40°/sin40°
=√3