Proving a Tangential Trig Identity

[Char. Limit]

Homework Statement

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

$$tan^{-1}(\alpha) - tan^{-1}(\beta) = tan^{-1}\left(\frac{\alpha-\beta}{1+\alpha \beta}\right)$$

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.

 

[tiny-tim]

Hi Char!

If α = tanX and β = tanY, it says tan(X - Y) = (tanX - tanY)/(1 + tanXtanY)

 

[Char. Limit]

Hi Char!

If α = tanX and β = tanY, it says tan(X - Y) = (tanX - tanY)/(1 + tanXtanY)

Hello tiny-tim!

Oh wow, it does. Thanks!