Prove2Me

Lean-Workbook Plus 71483: Trigonometric identity

Proved
WorkbookRestored.plus_71483

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

lean-workbookrestored-importssource-checked

For real x,yx,y, if cos⁡x=cos⁡y\cos x=\cos y and sin⁡x=−sin⁡y\sin x=-\sin y, then sin⁡2((x+y)/2)=0\sin^2((x+y)/2)=0.

Source: Lean-Workbook row lean_workbook_plus_71483 (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_71483 (x y : ℝ) (h₁ : Real.cos x = Real.cos y) (h₂ : Real.sin x = -Real.sin y) : (Real.sin ((x + y) / 2))^2 = 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_71483; immutable original Prove2Me node 52b7cd98-02cb-4abb-835a-021896af5637

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