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Nowadays, I realized that I'm interested in trigonometry and analytic trigonometry, which would be hard for my level. However, being curious makes whole things possible. Therefore, I'd like to get your book advices regarding trigonometric equations as well as multivariable trigonometric equations. For instance,

$$\cos (x)\cos (y)-\cos (x+y) = \dfrac{3}{2} \tag {1}$$

This question belong to pre-university calculus. As far as I can see, there are two variables in this equation. Thus, I couldn't find any similar equation on other trigonometric books I have.

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  • $\begingroup$ You don't need any particular book, any good book on trigonometry is fine but it is important that you understand the basic concept and definition and derive by yourself all the main trigonometric identities. $\endgroup$ – gimusi Jun 22 '18 at 12:43
  • $\begingroup$ See the references in the comments to Is there a “rigorous” book on “complete” trigonometry?, including the references at the web pages that the comments provide links to. $\endgroup$ – Dave L. Renfro Jun 22 '18 at 14:05
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The book you want (I think) is Trigonometry by I.M. Gelfand and ‎Mark Saul.

Another old classic from 1893 is worth a look as it has some great derivations: Sidney Luxton Loney's Plane Trigonometry Vols I, II which you can get both volumes as a reprint. (Apparently Ramanujan mastered these as a boy!) Here's a link, to Volume I+II, 2nd ed, and a link to the solution book for volume II.

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