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Math Help - relation between tan theta and tan 2theta

  1. #1
    Junior Member
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    relation between tan theta and tan 2theta

    I have got a question on the relation between [LaTeX ERROR: Convert failed] and [LaTeX ERROR: Convert failed]


    The question consists of two parts:
    The first pary asks me to solve the equation [LaTeX ERROR: Convert failed]
    Then I 've got the correct ans, which is

    [-1 + (1+a^2)^1/2]
    _________________
    a

    or

    [-1 - (1+a^2)^1/2]
    _________________
    a


    Then the second part ask me to express [LaTeX ERROR: Convert failed] in terms of [LaTeX ERROR: Convert failed] and the ans is

    [-1 + (1+ (tan 2 theta) ^2 )^1/2]
    ___________________________________
    a

    or

    [-1 - (1+ (tan 2 theta) ^2 )^1/2]
    ___________________________________
    a
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  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
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    someplace
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    4
    <br />
\tan(2\theta)=\frac{\sin(2 \theta)}{\cos(2 \theta)}=\frac{2\sin(\theta)\cos(\theta)}{(\cos( \theta ))^2-(\sin(\theta))^2}<br />

    So:

    <br />
\frac{1}{\tan(2\theta)}=\frac{1}{\tan(\theta)}-\tan(\theta)<br />

    then multiplying through by \tan(\theta) and rearranging gives:

    <br />
(tan(\theta))^2+\frac{1}{\tan(2 \theta)}\tan(\theta)-1=0<br />

    from which (if the algebra has been done right) the required result should
    follow from the application of the previous result or the quadratic formula.

    RonL
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