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
  • 1 month ago
    Favourite answer

    The answer is as follows:

    Attachment image
  • Pope
    Lv 7
    1 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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