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Thread: Having trouble with proving a trig identity

  1. #1
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    Having trouble with proving a trig identity

    Hi,


    I'm working on a trigonometry unit at the moment, and after going through the current lesson several times I still feel like I'm missing some things. I'm working on proving an identity right now that has me stumped, I tried resorting to using an online solver but in the steps it is telling me to use an identity that I'm unfamiliar with.


    Here is the problem:


    sinx + sinx(cotx^2) = cscx


    Immediately I'm lost, I tried switching cotangent for 1/sinx^2/cosx^2 or cosx^2/sinx^2 and neither of those seemed to help.


    The online solver told me to use the identity: cotx^2 = -1 + cscx^2 but this hasn't been mentioned in the lesson text and I don't expect it to be. I've tried to see how I could relate it to some of the other identities they have provided but I've had no luck. Are there any other identities like this one that should be remembered for future use? Also is this my best/only way of solving this? If so please let me know this looks.


    LEFT


    sinx + sinx(-1 + cscx^2)


    sinx - sinx + sinxcscx^2


    sinxcscx^2


    sinxcscx


    sinx(1/sinx)


    1


    RIGHT


    cscx


    cscx/cscx


    1


    Thank you for your help
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  2. #2
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    Re: Having trouble with proving a trig identity

    $\cot^2(x) = \left(\dfrac{\cos(x)}{\sin(x)}\right)^2 = $

    $\dfrac{\cos^2(x)}{\sin^2(x)} =$

    $\dfrac{1-\sin^2(x)}{\sin^2(x)} = $

    $\dfrac{1}{\sin^2(x)} - 1 = $

    $\csc^2(x) - 1$

    so you would have had to add just a few more lines of derivation to what you did to be able to honestly use that identity.
    Thanks from jpompey
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  3. #3
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    Re: Having trouble with proving a trig identity

    Thanks very much, I think I understand it now.
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