Derivation of the half-side tangent formulas via lagrange’s theorem (For polar spherical triangles)

Abstract

Spherical Geometry is a non-Euclidean geometry that provides good tools for terrestrial location and has great applicability in Astronomy. For this reason, trigonometry in spherical triangles is an interesting subject to study. Because it is a well-developed field, there are many widely known theorems and formulas with classical demonstrations. This article aims to present an alternative proof for the Half-Side Tangent Formulas, using the Langrange’s Theorem concerning polar triangles.