I'm looking for a good and detailed guide for trigonometric inequalities in pdf if possible.
Any recommended resources?

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3 Answers
Here are a few resources:
Trigonometric Identities and Inequalities: A Preview of Fourier Analysis (Payne, 2007)
Trigonometrical identities and inequalities (Holland, 2010)
Solving Trigonometric Inqualities (Nguyen)
Trigonometric inequalities and identities sound like an old math topic. Unless you are interested in fourier analysis then the kind of identities and inequalities are new and advanced. There might be a journal to devoted specifically to study this kind of math. One is mathematical inequalities and applications. It is free and online journal. I don't understand most of them. Most trig identities and inequalities you want to know about can be found in math competition site. I knew some authors with significant contribution to this area of math. For example, Titu Andresscu who has written some books for AMC, AMOP, etc.. about trigonometry. So search the web and enjoy yourself !

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