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## Homework Statement

I was reading on the Weierstrass substitution, and I came across the following trigonometric identity:

[tex]tan^{-1}(\alpha) - tan^{-1}(\beta) = tan^{-1}\left(\frac{\alpha-\beta}{1+\alpha \beta}\right)[/tex]

## Homework Equations

I'm not really sure which equations are applicable here.

## The Attempt at a Solution

What my question is is "how is this proven?". And try as I might, I don't see a way to prove this. Any help would be deeply appreciated.