Prove2Me

Lean-Workbook Plus 56081: Trigonometric identity

Proved
WorkbookRestored.plus_56081

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

lean-workbookrestored-importssource-checked

1(2−cos⁡x)(3−cos⁡x)=12−cos⁡x−13−cos⁡x\frac{1}{\left(2-\cos x\right)\left(3-\cos x\right)}=\frac{1}{2-\cos x}-\frac{1}{3-\cos x}.

Source: Lean-Workbook row lean_workbook_plus_56081 (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_56081 (x : ℝ) : (1 : ℝ) / ((2 - Real.cos x) * (3 - Real.cos x)) = 1 / (2 - Real.cos x) - 1 / (3 - Real.cos x)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_56081; immutable original Prove2Me node 0965b1d2-3613-4ddf-9e2e-f0bcf611cae2

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