Tangential Trig Identity

  • #1
Char. Limit
Gold Member
1,216
22

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.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi Char! :smile:

If α = tanX and β = tanY, it says tan(X - Y) = (tanX - tanY)/(1 + tanXtanY) :wink:
 
  • #3
Char. Limit
Gold Member
1,216
22
Hi Char! :smile:

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

Hello tiny-tim!

Oh wow, it does. Thanks!
 

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