1. The problem statement, all variables and given/known data The question is to show that Cos^2(x) + Sin^2(y) = 1 is an equivalence relation. 3. The attempt at a solution I know that there are three conditions which the equation must satisfy. (reflexivity, symetry, transitivity) For reflexivity I tried: Cos^2(x) - Cos^2(x) = Sin^2(y) - Sin^2(y) = 0. For symmetry: ( I don't fully understand this condition) I think that maybe Sin^2(y) + Cos^2(x) = 1 will do. Why? I'm not sure. Any explanation will be very apreciated. Transitivity: Cos^2(x) + Sin^2(y) = 1, Sin^2(y) + Cos^2(z) = 1, Cos^2(z) + Sin^2(h) = 1. If I add all o them I'll get Cos^2(x) + Sin^2(y) + Sin^2(y) + Cos^2(z) + Cos^2(z) + Sin^2(h) = 1 + 1 + 1 I was tempted to say that Sin^2(y) = Sin^2(z) = Sin^2(h), and that cos^2(x) = cos^2(z) (my thought was: "since they are supposed to be equivalent...") and rewrite it as: 3Cos^2(x) + 3Sin^2(h) = 3 (and then I divide it by 3) Cos^2(x) + Sin^2(h) = 1. I think my methods are wrong. Any help will be very appreciated.