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    http://www.mei.org.uk/files/papers/2012_Jan_c4.pdf

    its all of q8 but especially part 2, can someone give me the step by step as even mark scheme isnt making sense
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    You'll need to be a little more specific.
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    i get up to 3rd point of the mark scheme, then i dont get how we get to tan2 theta double angle from there, and from that i have no idea about the next part from that
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    (Original post by liverpool2044)
    i get up to 3rd point of the mark scheme, then i dont get how we get to tan2 theta double angle from there, and from that i have no idea about the next part from that
    Remember the identity that \displaystyle \tan 2\theta = \frac{2\tan \theta}{1 - \tan^2 \theta}.

    Now you know that your gradient of QP is \frac{4t}{2t^2 - 2} = \frac{2t}{t^2 - 1}. But from part (i) you know that \tan \theta = \frac{1}{t} \Rightarrow t = \frac{1}{\tan \theta}.

    So substitute this into your QP:

    \displaystyle

\begin{equation*} \frac{\frac{2}{\tan \theta}}{\frac{1}{\tan^2 \theta} - 1} = \cdots = \frac{2 \tan \theta}{1 - \tan^2 \theta}\end{equation*}

    After some simplification and common denominators and cancelling common factors, etc...

    But you know exactly what that identity is, so QP = \tan 2\theta

    Does this help at all?
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    (Original post by Zacken)
    Remember the identity that \displaystyle \tan 2\theta = \frac{2\tan \theta}{1 - \tan^2 \theta}.

    Now you know that your gradient of QP is \frac{4t}{2t^2 - 2} = \frac{2t}{t^2 - 1}. But from part (i) you know that \tan \theta = \frac{1}{t} \Rightarrow t = \frac{1}{\tan \theta}.

    So substitute this into your QP:

    \displaystyle

\begin{equation*} \frac{\frac{2}{\tan \theta}}{\frac{1}{\tan^2 \theta} - 1} = \cdots = \frac{2 \tan \theta}{1 - \tan^2 \theta}\end{equation*}

    After some simplification and common denominators and cancelling common factors, etc...

    But you know exactly what that identity is, so QP = \tan 2\theta


    Does this help at all?
    thank very helpful, its the few marks after too where it begins to ask about tpq can you help with that?
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    doesnt make sense
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    (Original post by liverpool2044)
    thank very helpful, its the few marks after too where it begins to ask about tpq can you help with that?
    if you extend the tangent line as far as the x axis and then consider the angles in the resulting triangle...
 
 
 
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