[REOPENED] I would like this question:
http://math.stackexchange.com/questions/243115/field-extensions-of-cos-and-sinhttps://math.stackexchange.com/questions/243115/field-extensions-of-cos-and-sin
to be reopened. The question was closed as a duplicate of Degree of field extensionDegree of field extension. Bit IMO, the questions are different. The closed one is about whether a specific proof is correct, not just a question about how to prove it (like the other question).