Can someone show me a full explanation of how:
(xcscx+1)/(xcscx) = (sinx/x)+1
Thank you!
Help with Basic Trig Identities?
2020-08-13 2:20 am
回答 (2)
2020-08-13 2:35 am
This is not what you wrote, but do you mean this?
[xcsc(x) + 1]/[xcsc(x)] = sin(x)/x + 1
LHS
= [xcsc(x) + 1]/[xcsc(x)]
= xcsc(x)/[xcsc(x)] + 1/[xcsc(x)]
= 1 + sin(x)/x
= RHS, for x ≠ kπ for any integer k
It is an identity only subject to the exclusion that I added. It cannot be an identity anywhere csc(x) is undefined, and we can brook no division by zero.
[xcsc(x) + 1]/[xcsc(x)] = sin(x)/x + 1
LHS
= [xcsc(x) + 1]/[xcsc(x)]
= xcsc(x)/[xcsc(x)] + 1/[xcsc(x)]
= 1 + sin(x)/x
= RHS, for x ≠ kπ for any integer k
It is an identity only subject to the exclusion that I added. It cannot be an identity anywhere csc(x) is undefined, and we can brook no division by zero.
收錄日期: 2021-04-18 18:36:45
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20200812182058AA8OxQg