logDeriv_sin — Mathlib

English

The logarithmic derivative of the complex sine is the cotangent: logDeriv(Complex.sin) = Complex.cot.

Русский

Логарифмическая производная модуля синуса комплексного равна котангенсу: logDeriv(Complex.sin) = Complex.cot.

LaTeX

$$$\logDeriv(\mathrm{Complex}.\sin) = \mathrm{Complex}.\cot$$$

Lean4

@[simp]
theorem logDeriv_sin : logDeriv (Complex.sin) = Complex.cot :=
  by
  ext
  rw [logDeriv, Complex.deriv_sin, Pi.div_apply, Complex.cot]

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