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Math Help - Proving Identities

  1. #1
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    Post Proving Identities

    How do I prove the following identity?

    cosx (secx - cscx) = 1 - cotx

    For the left side, I am at:

    cosx (1/cosx - 1/sinx)

    Am I anywhere near being right so far? Or is there an easier way to simplify the identity?
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  2. #2
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    Its a really good start

    \cos(x) \left(\frac{1}{\cos(x)} - \frac{1}{\sin(x)}\right)

    now expanding \cos(x) in you get

    \frac{\cos(x)}{\cos(x)} - \frac{\cos(x)}{\sin(x)}

    Spoiler:

    and simplifying

    1- \frac{1}{\tan(x)}

    1- \cot(x)
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Its a really good start

    \cos(x) \left(\frac{1}{\cos(x)} - \frac{1}{\sin(x)}\right)

    now expanding \cos(x) in you get

    \frac{\cos(x)}{\cos(x)} - \frac{\cos(x)}{\sin(x)}

    Spoiler:

    and simplifying

    1- \frac{1}{\tan(x)}

    1- \cot(x)
    Thanks so much. I just get so confused with the simplifying!
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  4. #4
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    Smile easier answer O_o

    hi there ) we are now at that leeson.,and I am proud to say that I'm able to answer your question..and I have an easier way to answer it..here it is:

    cos (sec-csc) = 1-cot (start at the left side)
    cos sec - cos csc = 1-cot (distribute)
    cos(1/cos) - sin/tan(1/sin) = 1-cot (cancel cos and sin)
    1-1/tan = 1-cot
    1-cot = 1-cot
    and that's it!!!

    At first, I am also confused with that..but I keep on researching until I learned it!!! hehe..

    I hope that I helped you..
    O_o
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