F.4 math------0-0-0-
2010-02-06 3:43 am
Given that A+B+C = 90 degree, prove that cotA + cotB + cotC = cotAcotBcotC
回答 (1)
2010-02-06 5:45 am
✔ 最佳答案
Given that A+B+C = 90 degree, prove that CotA +CotB +CotC =CotACotBCotC
Sol
A+B+C=90度
A+B=90度－C
Cot(A+B)=(CotACotB－1)/(CotA+CotB)
Cot(A+B)=Cot(90度－C)=TanC=1/CotC
So
1/CotC=(CotACotB－1)/(CotA+CotB)
CotC(CotACotB－1)=CotA+CotB
CotACotBCotC－CotC=CotA+CotB
CotA+CotB+CotC=CotACotBCotC
收錄日期: 2021-04-13 17:05:38
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100205000051KK01175