This inequality, in turn, rewrites as , where we set , and . Now, in order to prove this inequality, according to Lemma 1 it is sufficient to show that the numbers x, y, z are nonnegative and and satisfy yz + zx + xy = 1. The nonnegativity is trivial; the fact that the numbers x, y, z are all is clear, since they are the cotangenses of the angles A', B', C' which are all (this follows from the definition of these angles: , and ).
See ebavõrdsus, mis omakorda rewrites nagu Kui me seame , ja . Nüüd, et tõestada selle ebavõrdsuse järgi Lemma 1 piisab näidata, et arvu x, y, z on nonnegative ja ja vastavad yz + zx + xy = 1. Nonnegativity on triviaalne ning asjaolu, et arvud x, y, z on kõik On selge, sest nad on cotangenses nurkade A, B, C ", mis on kõik (see tuleneb mõiste need nurgad: , ja ).