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<ASB > <BSC cos \delta + <CSA cos \phi

Source: XII All-Ukrainian Tournament of Young Mathematicians, Qualifying p15

May 27, 2021
geometrytrigonometry3D geometrygeometric inequalityUkrainian TYM

Problem Statement

Given a triangular pyramid SABCSABC, in which ∠BSC=α\angle BSC = \alpha, ∠CSA=β\angle CSA =\beta, ∠ASB=γ\angle ASB = \gamma, and the dihedral angles at the edges SASA and SBSB have the value of ϕ\phi and δ\delta, respectively. Prove that γ>α⋅cos⁡δ+β⋅cos⁡ϕ.\gamma > \alpha \cdot \cos \delta +\beta \cdot \cos \phi.$
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