Shape_of_Tangent_Function

Proved

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

analysismonotonicityproofwikitrigonometry

The tangent function is strictly increasing on (-pi/2, pi/2).

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 Shape_of_Tangent_Function : StrictMonoOn Real.tan (Set.Ioo (-(Real.pi / 2)) (Real.pi / 2)) := by sorry

Source

https://proofwiki.org/wiki/Shape_of_Tangent_Function

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