2

I have learnt elementary trigonometric functions and inverse trigonometric functions. But the materials in my textbook isn't enough for me to gain a deeper understanding. I want to book that provides proofs of various inverse trigonometric formulas and related stuffs. I have already tried some books eg., S. L Loney's Book and some others. I want a book that provides proof for $\tan^{−1}x+\tan^{−1}y=π+\tan^{-1}\frac{x+y}{1−xy}$ when $xy>1$ and related inverse trigonometric formulas. Thank you!

Arturo Magidin
  • 398,050
Nazmul Hasan Shipon
  • 354
  • See Good book on advanced trig. – Dave L. Renfro Sep 28 '21 at 19:13
  • @DaveL.Renfro Based on the question I think these books mostly covers non-Euclidean spaces: spherical trig, hyperbolic trig. – Nazmul Hasan Shipon Sep 28 '21 at 19:15
  • The question suggested spherical trig and hyperbolic trig, but the books in the answer do not appear to be "mostly" about that. You could actually take a look before deciding. – David K Sep 28 '21 at 19:25
  • Based on the question I think these books mostly covers non-Euclidean spaces ---The books in my answer there were not selected for the other OP's additional request (although 3 of the 4 books I mentioned cover a fair amount about hyperbolic trig. functions). The books I gave there, at least (a different) 3 of them, are very well known and frequently cited here for math contest level trig. Incidentally, freely available copies of various editions of Hobson's book are on the internet (here, for example). – Dave L. Renfro Sep 28 '21 at 19:42
  • @DaveL.Renfro, I have looked upon the Hobson's book but couldn't find the proof of the exact formula I have mentioned above (the formulas in page 55 isn't what I was looking for). I wanted something more dedicated to this specific topic. – Nazmul Hasan Shipon Sep 28 '21 at 19:44
  • See also the books mentioned at Is there a "rigorous" book on "complete" trigonometry? Regarding "I wanted something more dedicated to this specific topic", I don't think you'll find anything better than the books in the links I've given, but there might be some expository papers or unpublished manuscripts. If I come across any, I'll let you know. – Dave L. Renfro Sep 28 '21 at 20:01
  • 1
    Just now, by accident, I happened to see a relatively complete discussion of the inverse tangent identity you asked about. See pp. 134-135 in The Elements of Plane Trigonometry (1892) by Rawdon Levett (1843-1923) and Charles Davison (1858-1940) -- internet archive and google-books. You'll need to look somewhere earlier in the book to see what their convention is for the use of upper case 'T' and lower case 't' in the tangent function designations. – Dave L. Renfro Nov 06 '21 at 06:49
  • Thank you @DaveL.Renfro. – Nazmul Hasan Shipon Nov 06 '21 at 13:05
  • In case you're still interested in book references, I just came across one that might be of interest. See pages 38-39 & 193-205 (and maybe pages 92 & 394) in A Problem Book In Algebra by Krechmar (1978). Although this isn't a traditional textbook, complete solutions are provided for all the problems, in particular for the problems involving inverse trigonometric functions on the pages I cited. – Dave L. Renfro Sep 04 '22 at 20:36

0 Answers0