Other trigonometric proofs of Pythagoras theorem

TL;DR

This paper presents new trigonometric proofs of the Pythagoras theorem by geometrically establishing the half-angle formula, challenging previous beliefs about the limitations of trigonometric proofs.

Contribution

It introduces novel geometric trigonometric proofs of the Pythagoras theorem using the half-angle formula, expanding the methods available for such proofs.

Findings

New geometric trigonometric proofs of Pythagoras theorem

Establishment of the half-angle formula geometrically

Challenging prior assumptions about proof possibilities

Abstract

Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\cos\theta=1-2\sin^2 \frac{\theta}{2}$.