Prove that sin2x/1-cos2x=cotx?
回答 (1)
2016-07-20 8:27 pm
L.H.S.
= sin(2x) / [1 - cos(2x)]
= 2 sin(x) cos(x) / [1 - 1 + 2 sin²(x)]
= 2 sin(x) cos(x) / [2 sin²(x)]
= cos(x) / sin(x)
= cot(x)
= R.H.S.
Hence, sin(2x) / [1 - cos(2x)] = cot(x)
= sin(2x) / [1 - cos(2x)]
= 2 sin(x) cos(x) / [1 - 1 + 2 sin²(x)]
= 2 sin(x) cos(x) / [2 sin²(x)]
= cos(x) / sin(x)
= cot(x)
= R.H.S.
Hence, sin(2x) / [1 - cos(2x)] = cot(x)
收錄日期: 2021-04-20 16:27:58
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160720121657AAuIdc2