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My math book has a trigonometry identity $\frac{2\cos2x}{\cos x}$ and they simplify it to $2\cos^2x-1$ but do not show the steps. I have tried many time to simplify but can never get the same answer.

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    Doesn't look true: [see this](http://www.wolframalpha.com/input/?i=%282cos%282x%29%29%2Fcos%28x%29+-%282cos^2%28x%29-1%29)2012-09-02
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    $2\cos^2x-1$ is identically equal to $\cos(2x)$, which is definitely NOT identically equal to $2\cos(2x)/\cos x$. Someone has a typo. (Or worse than a typo ... I'm not even seeing what the book *might have* intended.)2012-09-02
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    $\frac{2\cos2x}{\cos x}$ is an expression; it is not an identity. Where's the equal sign?2012-09-02

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