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Math Help - Need help with arctan

  1. #1
    Junior Member
    Joined
    Sep 2009
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    Need help with arctan

    I have some problems calculating problems like:
    arctan 2 + arctan 3 (answer cannot contain cyclometric functions)
    arctan(1+sqrt(2)) + arctan(1-sqrt(2)) (answer cannot contain cyclometric functions)

    Any hint would be appreciated.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, Sabo!

    I'll do the first one.

    I assume you know: . \tan(A + B) \:=\:\frac{\tan(A) + \tan(B)}{1-\tan(A)\tan(B)}


    Evaluate: . \arctan 2 + \arctan 3

    Let: . \theta \;=\;\arctan 2 + \arctan 3

    Then: . \tan\theta \;=\;\tan\bigg[\arctan 2 + \arctan 3\bigg] \;=\;\frac{\tan(\arctan 2) + \tan(\arctan 3)}{1 - \tan(\arctan 2)\tan(\arctan 3)}

    . . . . . \tan\theta \;=\;\frac{2+3}{1-2\cdot3} \;=\;\frac{5}{-5} \;=\;-1


    Therefore: . \theta \;=\;\arctan(-1) \;=\;\begin{Bmatrix}\dfrac{3\pi}{4} + \pi n \\ \\[-3mm] 135^o + 180^on \end{Bmatrix}

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  3. #3
    Junior Member
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    Sep 2009
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    Ah, so simple. Well, it usually is, isn't it? =)

    Thanks a lot!
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