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Math Help - proving trigonometric identity

  1. #1
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    proving trigonometric identity

    Write the following expression in either sine or cosine

     1) sin^2x+ cos^2x * cscx

    Attempt:
      sin^2 + cos^2 * \frac{1}{sinx}
      sin^2 + \frac{cos^2}{sinx}
    \frac{sin^2x}{1} + \frac{cos^2}{sinx}
    \frac{sin^3x+cos^2}{sinx}
     sin^3 +cos^2 * \frac{1}{sinx}
     1*1=1


    Can you please answer this question too
     cosx +sin^2x* secx

    Are my above steps correct please write in step if they are incorrect.
    Thank you very much!
    Last edited by mj.alawami; February 16th 2009 at 02:55 AM.
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Write the following expression in either sine or cosine

     1) sin^2x+ cos^2x * cscx

    Attempt:
     sin^2 + cos^2 * \frac{1}{sinx}
     sin^2 + \frac{cos^2}{sinx}
    \frac{sin^2x}{1} + \frac{cos^2}{sinx}
    \frac{sin^3x+cos^2}{sinx}
     sin^3 +cos^2 * \frac{1}{sinx}
     1*1=1


    \frac{sin^3x+cos^2}{sinx}

     <br />
=\frac{sin^3x-sin^2x+1}{sinx}<br />
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by mj.alawami View Post
    Write the following expression in either sine or cosine

     1) sin^2x+ cos^2x * cscx

    Attempt:
     sin^2 + cos^2 * \frac{1}{sinx}
     sin^2 + \frac{cos^2}{sinx}
    \frac{sin^2x}{1} + \frac{cos^2}{sinx}
    \frac{sin^3x+cos^2}{sinx}
    _______________________________________
     (sin^3 +cos^2 )* \frac{1}{sinx}
    _______________________________________
    ___________________________
     1*1=1
    __________________________

    Can you please answer this question too
     cosx +sin^2x* secx

    Are my above steps correct please write in step if they are incorrect.
    Thank you very much!
    -First of all watch the step in Red (correct)

    -Now watch the step in Green (incorrect)

    If your question is (doubtful since not a very good use of bracket)

     cosx +sin^2x* secx


    = \frac{sin^2(x) }{cos(x)} +cos(x)


     <br />
= \frac{sin^2(x) +cos^2(x)}{cos(x)}<br /> <br />

    Since
     <br />
sin^2(x) +cos^2(x) =1

     <br />
= \frac{1}{cos(x)}<br />
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