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Math Help - Using algebra to prove an identity

  1. #1
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    Exclamation Using algebra to prove an identity


    Use algebra to prove the identity.


    I can't seem to get a 1 on the numerator of the left equation. Here is what I got:

    (cosx/1-sin x) - tan x = 1/cos x
    (cosx/1-sin x) - sinx/cosx = 1/cos x
    (Minus both equations so it looks something like this)
    ((cosx)(cosx) - sin(1-sin t))/((1-sinx)(cosx))

    After the last stage no matter what I do I cannot get just a 1 on the numerator of the left equation. I have tried multiplying out the (cosx)(cosx) to become cos^2x and turning that into -sin^2x + 1 but still I would have a sin left on the top. Please help me with this. Thank you very much!
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by florx View Post

    Use algebra to prove the identity.


    I can't seem to get a 1 on the numerator of the left equation. Here is what I got:

    (cosx/1-sin x) - tan x = 1/cos x
    (cosx/1-sin x) - sinx/cosx = 1/cos x
    (Minus both equations so it looks something like this)
    ((cosx)(cosx) - sin(1-sin t))/((1-sinx)(cosx))

    After the last stage no matter what I do I cannot get just a 1 on the numerator of the left equation. I have tried multiplying out the (cosx)(cosx) to become cos^2x and turning that into -sin^2x + 1 but still I would have a sin left on the top. Please help me with this. Thank you very much!
    The fourth line of the attempt you made should look like this:

    \frac{cosx(cosx) - sinx(1-sinx)}{cosx(1-sinx)}

    = \frac{cos^2x - sinx +sin^2x}{cosx(1-sinx)}

    try taking it further now!
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  3. #3
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    Wow I used to just cancel out the (1 - sinx) right there and then so that is why I never got the correct answer. Thank you so much for your persistence in helping me!
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