Prove2Me

Lean-Workbook Plus 80943: Trigonometric identity

Proved
WorkbookRestored.plus_80943

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

lean-workbookrestored-importssource-checked

sin⁡(a+b−2c)cos⁡b−sin⁡(a+c−2b)cos⁡c\sin(a+b-2c) \cos b - \sin (a+c-2b) \cos c

=sin⁡(b−c){cos⁡(b+c−a)+cos⁡(a+c−b)+cos⁡(a+b−c)}= \sin (b-c) \{ \cos (b+c-a) + \cos (a+c-b) + \cos (a+b-c) \} .

Source: Lean-Workbook row lean_workbook_plus_80943 (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_80943 (a b c : ℝ) :
  Real.sin (a + b - 2 * c) * Real.cos b - Real.sin (a + c - 2 * b) * Real.cos c
  = Real.sin (b - c) * (Real.cos (b + c - a) + Real.cos (a + c - b) + Real.cos (a + b - c))   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_80943; immutable original Prove2Me node f94d3ef6-97b4-44c4-aa12-078058a9502e

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