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arXiv · 2406.01296

Algebraic relations between sine and cosine values

B. Adamczewski·É. Delaygue
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Abstract

The aim of this note is to show that any algebraic relation over $\overline{\mathbb{Q}}$ between the values of the trigonometric functions sine and cosine at algebraic points can be derived from the Pythagorean identity and the angle addition formulas. This result is obtained as a consequence of the Lindemann-Weierstrass theorem.

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B. Adamczewski, É. Delaygue. 2024-06-03. Algebraic relations between sine and cosine values. https://arxiv.org/abs/2406.01296

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