Cotangent Hecke Identity

Abstract

Partial closure of theorem 5.10: the cotangent double-angle identity.

Theorem 1.1 (The cotangent double-angle identity).

$$\forall theta\in \mathbb{R},\cot (theta)+\cot (theta+\frac{pi}{2})=2\cot (2theta)$$

Proof. Machine-checked in Lean as D5/S3/Fourier/CotangentHeckeIdentity.cotangent_double_angle (✓ std3). ∎

Source. Repository-derived.

Commentary.

This is the first, self-contained clause of the source theorem. The regularized-function equations, four corollaries, numerical certificates, and the later correction remain unresolved and are intentionally excluded from this partial closure.

References

• Truth anchor: D5/S3/Fourier/CotangentHeckeIdentity.cotangent_double_angle