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Math Help - Simplify [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]

  1. #1
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    Simplify [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]

    I need help simplifying this trig expression. I started by trying to find a common denom. btwn the two fractions
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  2. #2
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    Re: Simplify [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]

    Quote Originally Posted by hunnyelle View Post
    Simplify [(cosxcotx)/(secx+tanx)] + (sinx)/(secx-tanx)]

    I need help simplifying this trig expression. I started by trying to find a common denom. btwn the two fractions
    note that your common denominator, \sec^2{x} - \tan^2{x} equals 1


    btw ... do not double post.
    Last edited by skeeter; November 13th 2012 at 03:30 PM.
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    Re: Simplify [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]

    @skeeter: Yes , but then I'm left w/ (cosxcotx(secx-tanx) + sinx(sexc + tanx). I tried putting all of tht in terms of sin & cos & eventually reached the point [(cos^2x(cosx-sinx)+ sin^2x(1+sinx)]/(sinxcosx)]
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    MHF Contributor MarkFL's Avatar
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    Re: Simplify [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]

    Yes, when you double post, and your duplicate post gets deleted, then the help in the duplicate gets deleted as well, wasting time and effort of those trying to help.
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  5. #5
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    Re: Simplify [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]

    \cos{x}\cot{x}(\sec{x}-\tan{x}) + \sin{x}(\sec{x}+\tan{x})

    \cos{x}\cot{x}\sec{x} - \cos{x}\cot{x}\tan{x} + \sin{x}\sec{x} + \sin{x}\tan{x}

    \cot{x} - \cos{x} + \tan{x} + \sin{x}\tan{x}

    \cot{x}(1 - \sin{x}) + \tan{x}(1 + \sin{x})

    I don't think changing every term to sines and cosines will do much good from this point ... do you know what it is supposed to simplify to?
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  6. #6
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    Re: Simplify [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]

    The answer is cotx -cosx + tanx +sinxtanx, & I've figured out how to reach that answer!
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