# What are the alphas?

1. Mar 20, 2005

### bomba923

I wish I knew LaTex . But I know MathType!

Does such a pair of alphas exist?? (See the Below Thumbnail/attached image)
"Z" is the set of all integers

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2. Mar 20, 2005

### Zurtex

LaTeX is really easy to learn, just click on stuff people have wrote and it will show you the code. Check this thread out: https://www.physicsforums.com/showthread.php?t=8997

Correct me if I am wrong but your question simplifies down to:

$$\text{If} \, \alpha_1 \in \mathbb{Q} \, \, \, \text{does} \, \exists \, \alpha_2 \in \mathbb{Q}$$

Such that:

$$\tan \left( \alpha_1 \right) + \tan \left( \alpha_2 \right) = \frac{\pi}{3}$$

I'd guess not but to be honest I have no idea.

Oh and I think the question is wrong otherwise you could always let k=0.

Last edited: Mar 20, 2005
3. Mar 20, 2005

### Curious3141

Are we sure that that is supposed to be a tangent and not an arctangent ? I don't know of any "special" identities involving the arctangent of multiples of pi. The term in pi looks more suited to be the argument of the tangent function.

4. Mar 20, 2005

### Zurtex

Let $\alpha_1 = 1^c$

That should solve the problem.