By rigorous and complete I mean a book that contains proofs to all trig identities and formulas as well as those of hyperbolic geometry. I know there are proofs to most of these around the internet but is there a specific book or website that accomplishes this? Also, a geometric approach would be preferable.
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See my answers to Good book on advanced trig AND Reference Request: Book for Trigonometry and Geometry, and also this (admittedly biased) google search. – Dave L. Renfro May 07 '18 at 20:07
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Here are three other older books, besides those I cited above, that are pretty complete: A System of Plane and Spherical Trigonometry by Richard Wilson (1831); A Treatise on Plane Trigonometry by John Casey (1888); Éléments de Trigonométrie Plane et Sphérique [copy at google-books] by Émile Gelin (1888; most complete of these three). – Dave L. Renfro May 07 '18 at 20:24
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E. W. Hobson, A Treatise on Plane Trigonometry, Cambridge University Press, 1891. $\qquad$ – Michael Hardy May 07 '18 at 21:02