Talk:Sine of Integer Multiple of Argument/Formulation 3

In what way is this a corollary of Sine of Integer Multiple of Argument? --prime mover (talk) 11:45, 23 June 2020 (EDT)

There is already a page called "Sine of Integer Multiple of Argument". This relationship between $\map \sin {n \theta }$ and the sum of $\frac {\cos k \theta} {\cos^k \theta}$ is a pretty relationship and I wasn't sure where else to place it. If it was its own theorem, would the page title be "Sine of Integer Multiple of Argument Version 2"? Thoughts? --Robkahn131 (talk) 12:13, 23 June 2020 (EDT)

The point is that a corollary is a result which "comes for free" on the back of an existing result. If you have to prove it using a completely different proof technique which starts from scratch, then it's not a corollary.

There are precedents for sets of related results of a particular type. Naming is an art. "Variant" is a good option, "Version" is not because it's not a version. Names are better than numbers. --prime mover (talk) 12:18, 23 June 2020 (EDT)

Aaah! I see. Example: Axiom of Archimedes/Variant - I had not seen this before. Both "corollaries" here seem to be variants instead. Would you agree with this? --Robkahn131 (talk) 12:22, 23 June 2020 (EDT)

Or "formulation" -- call them "Formulation 1", "Formulation 2" and "Formulation 3" so you don't have the misleading idea of a "main theorem" and "variants" so much as $3$ independent results that stand alone in their own right. --prime mover (talk) 14:18, 23 June 2020 (EDT)