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Lean-Workbook Plus 14676: Trigonometric identity

Proved
WorkbookRestored.plus_14676

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

lean-workbookrestored-importssource-checked

Prove that sin(x+y)sin(y+z)=sin(y)sin(x+y+z)+sin(z)sin(x)sin(x+y)sin(y+z)=sin(y)sin(x+y+z)+sin(z)sin(x) .

Source: Lean-Workbook row lean_workbook_plus_14676 (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_14676 : ∀ x y z : ℝ, sin (x + y) * sin (y + z) = sin y * sin (x + y + z) + sin z * sin x   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_14676; immutable original Prove2Me node 4660f15f-1181-4f8c-a23b-4429a8d0be24

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