Prove2Me

Lean-Workbook Plus 37102: Trigonometric identity

Proved
WorkbookRestored.plus_37102

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

lean-workbookrestored-importssource-checked

For real a,b,c,Aa,b,c,A, bsin⁡A(a2+c2−b2−b2−c2+a2)2abc=bsin⁡A(2a2−2b2)2abc\frac{b\sin A(a^2+c^2-b^2-b^2-c^2+a^2)}{2abc}=\frac{b\sin A(2a^2-2b^2)}{2abc}.

Source: Lean-Workbook row lean_workbook_plus_37102 (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_37102 (a b c A : ℝ) : (b * Real.sin A * (a^2 + c^2 - b^2 - b^2 - c^2 + a^2)) / (2 * a * b * c) = (b * Real.sin A * (2 * a^2 - 2 * b^2)) / (2 * a * b * c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_37102; immutable original Prove2Me node fde68700-a4c0-42b1-9732-3be60d00da02

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