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Thread: Sum and Difference

  1. #1
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    Sum and Difference

    $\displaystyle
    \tan(A + B)={-7/6},
    \tan(B)={5/3}
    $

    Find tan(A)
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  2. #2
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    use the sum identity ...

    $\displaystyle \tan(a+b) = \frac{\tan{a} + \tan{b}}{1 - \tan{a}\tan{b}}$

    sub in what you know, solve for $\displaystyle \tan{a}$
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  3. #3
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    and how would i solve for tan(a), not sure where to start.
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  4. #4
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    $\displaystyle \tan(a+b) = \frac{\tan{a} + \tan{b}}{1 - \tan{a}\tan{b}}$

    $\displaystyle \tan(a+b) (1 - \tan{a}\tan{b}) = \tan{a} + \tan{b}$

    $\displaystyle \tan(a+b) - \tan(a+b) \tan{a} \tan{b} = \tan{a} + \tan{b}$

    $\displaystyle \tan(a+b) - \tan{b} = \tan{a} - \tan(a+b) \tan{a} \tan{b}
    $

    $\displaystyle \tan(a+b) - \tan{b} = \tan{a}[1 - \tan(a+b) \tan{b}]$

    $\displaystyle \frac{\tan(a+b) - \tan{b}}{1 - \tan(a+b) \tan{b}} = \tan{a}$
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