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Math Help - identity

  1. #1
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    identity

     \frac{(tan \theta + sec \theta -1 )}{(tan \theta - sec \theta +1 )}= tan \theta + sec \theta
    Last edited by z1llch; June 23rd 2009 at 06:18 AM. Reason: have no idea how to eliminate the one.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    The identity can be rewritten as:

    tan \theta+sec \theta - 1=(tan \theta-sec \theta+1)(tan\theta+sec\theta)

    tan \theta+sec \theta - 1=tan ^2\theta -sec \theta tan \theta + tan \theta + sec \theta tan\theta - sec^2\theta+sec \theta

    tan \theta+sec \theta - 1=tan^2\theta +tan\theta - sec^2\theta+sec \theta

    tan \theta+sec \theta -1=-1+tan\theta+sec\theta

    which is always true.
    Last edited by alexmahone; June 23rd 2009 at 06:50 AM.
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  3. #3
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    arent i suppose to use the left hand side only, and prove it is equal to the right hand side?
    Last edited by z1llch; June 23rd 2009 at 06:54 AM.
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by z1llch View Post
    arent i suppose to use the left hand side only, and prove it is equal to the right hand side?
    No; you can cheat.
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  5. #5
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    hahaha. i'm stuck with the number 1. guessed i'm supposed to use the cos2+sin2=1 formula to get rid of it, but do not know how. or maybe i;m wrong, there other way.
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  6. #6
    Member great_math's Avatar
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    Quote Originally Posted by z1llch View Post
     \frac{(tan \theta + sec \theta -1 )}{(tan \theta - sec \theta +1 )}= tan \theta + sec \theta
    We can write it as,

    \frac{\tan\theta+\sec\theta-1}{\tan\theta-\sec\theta+1}

    = \frac{\tan\theta+\sec\theta+\tan^2\theta-\sec^2\theta}{\tan\theta-\sec\theta+1}

    = \frac{(\tan\theta+\sec\theta)(\tan\theta-\sec\theta+1)}{\tan\theta-\sec\theta+1}

    = \tan\theta+\sec\theta
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by alexmahone View Post
    No; you can cheat.
    to prove an identity, you must work with one side at a time
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  8. #8
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    thank you great_math.
    took me an hour to come up with those lines this morning. but mine is way longer..
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