lean_workbook_plus_31644

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by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $\cos\theta + \sqrt{3}\sin\theta = 2\left(\cos\theta\cos\frac{\pi}{3} + \sin\theta\sin\frac{\pi}{3}\right)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_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

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