show that
(1-cosA)/sinA=sinA/(1+cosA)
數學題三角學
2012-01-08 3:20 am
回答 (2)
2012-01-08 3:52 am
✔ 最佳答案
(1 - cosA)/sinA=sinA/(1 + cosA)<=> (sinA)^2 = (1 - cosA)(1 + cosA)
<=> (sinA)^2 = 1 - (cosA)^2
<=> (sinA)^2 = (sinA)^2
which is true. So, (1 - cosA)/sinA=sinA/(1 + cosA)
2012-01-08 3:52 am
(1-cosA)/sinA - sinA/(1+cosA)
= [(1-cosA)(1+cosA) - sin^2 A]/[sinA(1+cosA)]
= [1 - cos^2 A - sin^2 A]/[sinA(1+cosA)]
= 0 for A =/= n180deg for n = 0,1,2,3,...
Therefore,
(1-cosA)/sinA = sinA/(1+cosA)
iff A =/= n180deg for n = 0,1,2,3,...
= [(1-cosA)(1+cosA) - sin^2 A]/[sinA(1+cosA)]
= [1 - cos^2 A - sin^2 A]/[sinA(1+cosA)]
= 0 for A =/= n180deg for n = 0,1,2,3,...
Therefore,
(1-cosA)/sinA = sinA/(1+cosA)
iff A =/= n180deg for n = 0,1,2,3,...
參考: Hope the solution can help you^^”
收錄日期: 2021-04-26 14:56:23
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120107000051KK01010