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Math Help - verifying identities...

  1. #1
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    Smile verifying identities...

    good evening again to all..

    please help me again about this proving problem..

    how would i verify that..

    [ 1 / cot x - csc x ] + [ 1 / cot x - csc x ] = 2 cot?????

    thanks.. ^^
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  2. #2
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    Quote Originally Posted by riasantos View Post
    good evening again to all..

    please help me again about this proving problem..

    how would i verify that..

    [ 1 / cot x - csc x ] + [ 1 / cot x - csc x ] = 2 cot?????

    thanks.. ^^
    You could start by either using brackets correctly or using LaTeX.

    Is it

    \frac{1}{\cot{x} - \csc{x}} + \frac{1}{\cot{x} - \csc{x}}

    or

    \frac{1}{\cot{x}} - \csc{x} + \frac{1}{\cot{x}} - \csc{x}?
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  3. #3
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    Smile

    it is the first one. ^^


    thanks for the reply.. ^^
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  4. #4
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    \frac{1}{\cot{x} - \csc{x}} + \frac{1}{\cot{x} - \csc{x}} = \frac{2}{\cot{x} - \csc{x}}

     = \frac{2(\cot{x} + \csc{x})}{(\cot{x} - \csc{x})(\cot{x} + \csc{x})}

     = \frac{2(\cot{x} + \csc{x})}{\cot^2{x} - \csc^2{x}}

     = \frac{2(\cot{x} + \csc{x})}{-1}

     = -2(\cot{x} + \csc{x})


    I don't know if you can go any futher...
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  5. #5
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    Is not this identity?

    \frac{1}{\cot x - \csc x} + \frac{1}{\cot x + \csc x} = -2\cot x

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  6. #6
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    Quote Originally Posted by danielomalmsteen View Post
    Is not this identity?

    \frac{1}{\cot x - \csc x} + \frac{1}{\cot x + \csc x} = -2\cot x

    That's not what the original question was...

    But if it IS this...

    \frac{1}{\cot{x} - \csc{x}} + \frac{1}{\cot{x} + \csc{x}}

     = \frac{\cot{x} + \csc{x}}{(\cot{x} - \csc{x})(\cot{x} + \csc{x})} + \frac{\cot{x} - \csc{x}}{(\cot{x} - \csc{x})(\cot{x} + \csc{x})}

     = \frac{\cot{x} + \csc{x} + \cot{x} - \csc{x}}{(\cot{x} - \csc{x})(\cot{x} + \csc{x})}

     = \frac{2\cot{x}}{\cot^2{x} - \csc^2{x}}

     = \frac{2\cot{x}}{-1}

     = -2\cot{x}.
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