Arctan of Product: How to Rewrite \arctan(a*b) Using the Product Rule?

[Niles]

Homework Statement

Hi

Say I have an expression $\arctan(a*b)$. Is there a product rule for $\arctan$ that I can use to rewrite this? I tried the Wiki-page, but I couldn't find one there.

 

[CompuChip]

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)?

 

[Niles]

Thanks. OK, so after some calculations I get an expression of the form
$$\arctan(\tan(A)B)$$
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 $\arctan$ when its argument is a sum.