A trigonometric approach to an identity by Ramanujan

TL;DR

This paper presents a trigonometric method to prove Ramanujan's identity by expressing it in polar coordinates, simplifying the proof to elementary trigonometric verification, and deriving new variations of the original identity.

Contribution

It introduces a novel trigonometric approach to Ramanujan's identity, providing alternative proofs and variations not previously explored.

Findings

Simplifies Ramanujan's identity proof using polar coordinates

Derives new variations of Ramanujan's original identity

Demonstrates elementary trigonometric verification as a proof technique

Abstract

An identity by Ramanujan is expressed using polar coordinates, so that its proof reduces to the verification of an elementary trigonometric identity. This approach produces a few variations on Ramanujan's original identity.