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Math Help - Expanding tan(x+2y)

  1. #1
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    Expanding tan(x+2y)

    I dunno what I'm doing wrong ><

    the answer is  \frac{\tan\chi - \tan\chi\tan^2\gamma +2\tan\gamma}{1 - \tan^2\gamma - 2\tan\chi\tan\gamma}

    Thanks in advance
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  2. #2
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    Quote Originally Posted by icesta1 View Post
    I dunno what I'm doing wrong ><

    the answer is  \frac{\tan\chi - \tan\chi\tan^2\gamma +2\tan\gamma}{1 - \tan^2\gamma - 2\tan\chi\tan\gamma}

    Thanks in advance
    Use the angle sum identity:

    \tan{(\alpha + \beta)} = \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}


    So \tan{\chi + 2\gamma} = \frac{\tan{\chi} + \tan{2\gamma}}{1 - \tan{\chi}\tan{2\gamma}}


    And now simplify the double angle using the identity:

    \tan{2\theta} = \frac{2\tan{\theta}}{1 - \tan^2{\theta}}.
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