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Math Help - Find the angle ?

  1. #1
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    Question Find the angle ?

    Hi!
    In this problem I need to find the exact value of tan(x) and the x=arctan7+2arctan 3. How can I find the angle for tan(x)?
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  2. #2
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    Quote Originally Posted by Kluringen View Post
    Hi!
    In this problem I need to find the exact value of tan(x) and the x=arctan7+2arctan 3. How can I find the angle for tan(x)?
    \tan{x} = \tan(\arctan{7} + 2\arctan{3})<br />

    \tan{x} = \frac{\tan(\arctan{7}) + \tan(2\arctan{3})}{1 - \tan(\arctan{7})\tan(2\arctan{3})}<br />

    intermediate step ...

    \tan(2\arctan{3}) = \frac{2\tan(\arctan{3})}{1 - \tan^2(\arctan{3})} = -\frac{3}{4}<br />

    evaluate ...

    \tan{x} = \frac{7 -\frac{3}{4}}{1 + \frac{21}{4}} = 1<br />
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