In mathematics, Hermite's cotangent identity is a trigonometric identity discovered by Charles Hermite.Warren P. Johnson, "Trigonometric Identities à la Hermite", American Mathematical Monthly, volume 117, number 4, April 2010, pages 311–327 Suppose a1, ..., an are complex numbers, no two of which differ by an integer multiple of . Let
(in particular, A1,1, being an empty product, is 1). Then
The simplest non-trivial example is the case n = 2:
Notes and references