Lean-Workbook Plus 31644: Trigonometric identity

Proved

WorkbookRestored.plus_31644

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

lean-workbookrestored-importssource-checked

For every real $\theta$ , $\cos\theta+\sqrt3\sin\theta=2(\cos\theta\cos(\pi/3)+\sin\theta\sin(\pi/3))$ .

Source: Lean-Workbook row lean_workbook_plus_31644 (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_31644 (θ : ℝ) :
  Real.cos θ + Real.sqrt 3 * Real.sin θ =
    2 * (Real.cos θ * Real.cos (Real.pi / 3) + Real.sin θ * Real.sin (Real.pi / 3))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_31644; immutable original Prove2Me node c59da304-be92-48d5-9172-ad8d266b3c2c

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