# Help with Basic Trig Identities?

Can someone show me a full explanation of how:

(xcscx+1)/(xcscx) = (sinx/x)+1

Thank you!

### 2 Answers

Relevance

- PopeLv 71 month ago
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.

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