Lean-Workbook Plus 6172: Trigonometric identity

Proved

WorkbookRestored.plus_6172

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

lean-workbookrestored-importssource-checked

Sum to product gives $\sin(20)+\sin(40)=2\sin(30)\cos(10)$

Source: Lean-Workbook row lean_workbook_plus_6172 (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_6172 : ∀ a b c d : ℝ, a = 20 ∧ b = 40 → c = 30 ∧ d = 10 → sin a + sin b = 2 * sin c * cos d   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_6172; immutable original Prove2Me node 14a89328-d548-4fc1-9ae6-878b103307fc

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