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Math Help - How to solve an equation

  1. #1
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    How to solve an equation

    The equation is:

    cotg(X) = (sqrt(3)*cos(50) + sin(50))*(1-2*sqrt(3)*cos(50)+2*sin(50)) /
    (sqrt(3)*sin(50) - cos(50))

    Using a calculator, I find X = 50.

    How to develop the equation to find the solution?

    Thanks.
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  2. #2
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    Re: How to solve an equation

    What do you mean by "develop" the equation? The right side is simply a number. Find that number and take its inverse cotangent.
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  3. #3
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    Re: How to solve an equation

    Doing what you propose with the calculator we arrive to 50 degrees.
    So, if X = 50, it would be possible to "develop" or simplify the trigonometric expression on the second member of the equation to arrive to cotg(50).
    Don't you think so, considering that in the expression we have only trigonometric functions of the same angle?
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: How to solve an equation

    Quote Originally Posted by TOZE View Post
    Don't you think so, considering that in the expression we have only trigonometric functions of the same angle?
    Consider any angle \alpha instead of 50^0 and expand \cot \alpha in the following way:

    \cot \alpha =\cot \;[30^0+(\alpha -30^0)]=\frac{\cot 30^0\cdot \cot (\alpha -30^0)-1}{\cot 30^0+\cot (\alpha -30^0)}=

    \frac{\sqrt{3}\cdot \dfrac{\cos (\alpha-30^0)}{\sin (\alpha-30^0)}-1}{\sqrt{3}+\dfrac{\cos (\alpha-30^0)}{\sin (\alpha-30^0)}}}=\ldots

    Let's see if you get the right side of the equation (with \alpha instead of 50^0 ).

    P.D. I haven't checked it, it is only a proposal.
    Last edited by FernandoRevilla; December 21st 2011 at 11:13 PM.
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