A Study on the Infinite Product Expansion of Trigonometric Identities via Recursive Sum-to-Product Factorization of n-th Roots

Key Points

• To explore the infinite product expansion of trigonometric identities through a specific recursive factorization method.
• Examination of trigonometric identities through infinite product forms.
• Application of recursive sum-to-product factorization techniques.
• Investigation of the relationship with n-th roots.
• Identification of novel infinite product expansions of trigonometric functions.
• Demonstration of connections between trigonometric identities and recursive factorization.
• Contribution to the understanding of mathematical properties of n-th roots in trigonometric contexts.