Prove the following
(1)
[ cscθ / (sinθ + cosθ) ] x [ (1+ 2sinθcosθ) / secθ ]= cotθ (sinθ + cosθ)
(2)
[cot^2 (3π/2 - θ) ] / [tan^2 (π+θ) - sec^2(π-θ)] = 1-sec^2θ
F.4 trigonometry-0-0-0-
2010-01-03 9:16 am
回答 (1)
2010-01-03 9:29 am
✔ 最佳答案
(1) [ cscθ / (sinθ + cosθ) ] x [ (1+ 2sinθcosθ) / secθ ]= [ cscθ / (sinθ + cosθ) ] x (sin θ + cos θ)2/sec θ
= csc θ (sin θ + cos θ)/sec θ
= cot θ (sin θ + cos θ)
(2) [cot2 (3π/2 - θ) ] / [tan2 (π+θ) - sec2 (π-θ)]
= tan2 θ/(tan2 θ - sec2 θ)
= tan2 θ/(tan2 θ - 1 - tan2 θ)
= - tan2 θ
= 1 - sec2 θ
參考: Myself
收錄日期: 2021-04-13 17:01:13
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100103000051KK00143