Human and automated approaches for finite trigonometric sums

TL;DR

This paper reviews existing identities involving finite trigonometric sums, proves two conjectures, and introduces an automated method for verifying such identities, enhancing understanding and proof techniques in the field.

Contribution

It clarifies the novelty of recent identities, proves two conjectures, and presents an automated approach for proving trigonometric sum identities.

Findings

Identities by Harshitha et al. are not new or are easily provable.

Two conjectures from the referenced paper are proven.

An automated approach for proving trigonometric identities is described.

Abstract

We show that identities involving trigonometric sums recently proved by Harshitha, Vasuki and Yathirajsharma, using Ramanujan's theory of theta functions, were either already in the literature or can be proved easily by adapting results that can be found in the literature. Also we prove two conjectures given in that paper. After mentioning many other works dealing with identities for various trigonometric sums, we end this paper by describing an automated approach for proving such trigonometric identities.