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Math Help - Find an expression

  1. #1
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    Find an expression

    hmmm...so i need to find an expression for the attached image...
    im getting tan((x^2-4)/4) but its wrong, what am I missing?

    Thanks in advance
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  2. #2
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    Quote Originally Posted by OakleyAddict View Post
    hmmm...so i need to find an expression for the attached image...
    im getting tan((x^2-4)/4) but its wrong, what am I missing?

    Thanks in advance
    Let \alpha = \cos^{-1} \left( \frac{2}{x} \right) \Rightarrow \cos \alpha = \frac{2}{x}. So you want the value of \tan^2 \alpha.

    Now note that \tan^2 \alpha = \frac{1}{\cos^2 \alpha} - 1. Make the necessary substitution and simplify.
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  3. #3
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    o ya srry,,, it says in terms of x so that doesn't work i think and it said yo use as a hint: tan^(2)+1=sec^2(x)
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  4. #4
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    Quote Originally Posted by OakleyAddict View Post
    so that doesn't work i think
    Yes it does. You haven't tried.
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  5. #5
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    Quote Originally Posted by OakleyAddict View Post
    o ya srry,,, it says in terms of x so that doesn't work i think and it said yo use as a hint: tan^(2)+1=sec^2(x)
    Am I to understand that you cannot (or haven't tried to) substitute \cos \alpha = \frac{2}{x} into the right hand side of \tan^2 \alpha = \frac{1}{\cos^2 \alpha} - 1 ?
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