Talk:Triple Angle Formulas/Tangent

Proof 2

There is a minor flaw in this proof. For any $\theta$ for which $\tan 2 \theta$ is undefined, it will follow that both $\tan \theta$ and $\tan 3 \theta$ are defined and the identity holds. For example, if $\theta=\dfrac{\pi}{4}$, then $2\theta=\dfrac{\pi}{2}$ and $3\theta=\dfrac{3\pi}{4}$. We then have $\tan \theta=1$ and $\tan 3 \theta=-1$ and the identity holds even in this case. But $\tan 2 \theta$ will be undefined meaning the proof is not valid in this case.

I am considering updating the proof to correct this flaw. However as I'm new to Proof Wiki, I wanted to check in here first before doing so. I'm not sure if this would be a welcome addition to this proof, or if my concern with the proof would be seen as too minor a flaw to be worth addressing and I'd be engaging in unwelcome nitpicking if I did so. So I'm looking for any guidance you might have to offer about making this kind of an update before I go ahead and do so. Dash1729 (talk) 18:00, 27 March 2024 (UTC)

If you see a flaw or something that you can improve, definitely fix it. That's assuming that you are still using the same basic idea as what is posted. If you are coming up with a completely differnt proof, then it would need to be a separate page. Most contributors (self included) are usually very appreciative of improvements/fixes. --Robkahn131 (talk) 22:15, 27 March 2024 (UTC)

Good catch. I have $\mathsf{Pr} \infty \mathsf{fWiki}$fied the source code to keep the style consistent. Excellent contribution. Many thanks. --prime mover (talk) 10:21, 28 March 2024 (UTC)