Prove2Me

Lean-Workbook Plus 40625: Trigonometric identity

Proved
WorkbookRestored.plus_40625

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

lean-workbookrestored-importssource-checked

If a=cos⁡αa=\cos\alpha and b=sin⁡α/3b=\sin\alpha/\sqrt3, then a2+3b2=1a^2+3b^2=1.

Source: Lean-Workbook row lean_workbook_plus_40625 (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_40625 (a b : ℝ) (α : ℝ) (h₁ : a = Real.cos α) (h₂ : b = Real.sin α / Real.sqrt 3) : a^2 + 3 * b^2 = 1   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_40625; immutable original Prove2Me node 53af00af-a3c1-4686-a89c-286871ec46a4

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