Prove2Me

Lean-Workbook Plus 75190: Trigonometric identity

Proved
WorkbookRestored.plus_75190

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For real xx, tan⁡(π/2−x)=1/tan⁡x\tan(\pi/2-x)=1/\tan x, using Lean’s total tangent and division.

Source: Lean-Workbook row lean_workbook_plus_75190 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
open Real
Formal statement
theorem WorkbookRestored.plus_75190 (x : ℝ) : tan (π/2 - x) = 1 / tan x   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_75190; immutable original Prove2Me node e0f137d9-ca6d-43e7-9477-903b38947f8d

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