Tangent_Function_is_Periodic_on_Reals

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

analysisperiodicityproofwikitrigonometry

tan(x + pi) = tan(x) for all real x where both are defined.

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic

Formal statement

import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic

theorem Tangent_Function_is_Periodic_on_Reals (x : ℝ) : Real.tan (x + Real.pi) = Real.tan x := by sorry

Source

https://proofwiki.org/wiki/Tangent_Function_is_Periodic_on_Reals

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