prove they'r equal:
(1+sinx)/cosx = (1+tan(x/2))/(1-tan(x/2))
plz show all step...thx..
prove
2007-12-07 2:17 pm
回答 (1)
2007-12-07 3:34 pm
✔ 最佳答案
LHS=(1+sinx)/cosx
=(1+2sin(x/2)cos(x/2))/(2cos^2(x/2)-1)
=(cos^2(x/2)+2sin(x/2)cos(x/2)+sin^2(x/2))/(2cos^2(x/2)-cos^2(x/2)-sin^2(x/2))
=(cos(x/2)+sin(x/2))^2/(cos(x/2)-sin(x/2))(cos(x/2)+sin(x/2))
=(cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2))
= (1+tan(x/2))/(1-tan( x/2)) [上下除cos(x/2)]
收錄日期: 2021-04-25 16:58:05
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071207000051KK00430