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Arctan of a product

  1. May 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Say I have an expression [itex]\arctan(a*b)[/itex]. Is there a product rule for [itex]\arctan[/itex] that I can use to rewrite this? I tried the Wiki-page, but I couldn't find one there.
  2. jcsd
  3. May 5, 2013 #2


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    There are some, Wikipedia lists
    $$\arctan \alpha \pm \arctan \beta = \arctan\left( \frac{\alpha \pm \beta}{1 \mp \alpha \beta} \right)$$

    Maybe you can ask a slightly more specific question (e.g. if you need this for a bigger problem, what is that problem)?
  4. May 5, 2013 #3
    Thanks. OK, so after some calculations I get an expression of the form
    I wanted to Taylor expand B to first order in order to simplify, but I thought that would only make sense if there was a neat way to express [itex]\arctan[/itex] when its argument is a sum.
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