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Math Help - Multiplication of fractions

  1. #1
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    Multiplication of fractions

    Hey,
    I have a small question about multiplication.
    From what I learned at school 1/5/6 equals to 6/5 (I moved 6 to the top)
    Is this always true ? How about this example:
    It is known that x/tanx equals
    x/(cox/sinx) equals
    x * 1/(cox/sinx)

    Is it legal to say it equals
    x * sinx/cosx ? (Move the sin upwards)

    Thanks a lot.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Multiplication of fractions

    The process you mention is true, however in your example with the tangent function, you would write:

    \frac{x}{\tan(x)}=\frac{x}{\frac{\sin(x)}{\cos(x)}  }=\frac{x\cos(x)}{\sin(x)}
    Last edited by MarkFL; December 22nd 2012 at 02:00 AM.
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  3. #3
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    Re: Multiplication of fractions

    (x*cosx)/(sinx) is defined in pi /2 (Equals to zero)
    According to what your saying, x/tanx is defined in pi/2 .. That is of course not true.
    So what is the right answer ?
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Multiplication of fractions

    I should have added for \cos(x)\ne0.

    I was simply pointing out that \tan(x)\ne\frac{\cos(x)}{\sin(x)} as you stated in your first post.
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  5. #5
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    Re: Multiplication of fractions

    Ok Thanks a lot
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  6. #6
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    Re: Multiplication of fractions

    also, while tan(x) is not defined at pi/2, we CAN define 1/tan(x) (another form of cot(x)) at pi/2, as 0 (this makes cot(x) continuous at 0).

    this often happens: we can define something that is a/(undefined) sometimes, in a way that "doesn't lead to contradictions". you do have to be careful with this, though.
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