International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 705-714
Department of Mathematics and Computer Science, University of Wisconsin, Whitewater 53190, Wisconsin, USA
Received 20 November 1985
Copyright © 1986 Malvina Baica. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper the author obtains new trigonometric identities of the form which are derived as a result of relations in a cyclotomic field , where is the field of rationals and is a root of unity.
Those identities hold for every positive integer and any proof avoiding cyclotomic fields could be very difficult, if not insoluble. Two formulasstated only by Gauss in a slightly different form without a proof, are obtained and used in this paper in order to give some numeric applications of our new trigonometric identities.