To strengthen trigonometry skills, several recommendations for in-depth problem-solving books are discussed. A dedicated trigonometry book, rather than a precalculus one, is preferred, with suggestions including a used edition by Larson, Hostetler, & Edwards, which is considered acceptable even if it's 12 to 30 years old. "Advanced Trigonometry" by C. V. Durell and A. Robson, published in 1930 and available as a Dover reprint, is highlighted for its depth, despite not introducing new concepts. For a more recreational approach, "Trigonometric Delights" by Eli Maor is recommended as an enjoyable read. Additionally, "Before Calculus" by Louis Leithold is mentioned as a valuable resource for self-studying precalculus.