Prove2Me

A trigonometric square identity

Proved
WorkbookSource.problem_33418

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Thus (1+sin⁡θ)(1+cos⁡θ)=12(1+sin⁡θ+cos⁡θ)2,(1+\sin \theta)(1+\cos \theta)=\frac{1}{2}(1+\sin \theta +\cos \theta)^2,

Source: InternLM Lean-Workbook, record lean_workbook_33418 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_33418 (θ : ℝ) : (1 + Real.sin θ) * (1 + Real.cos θ) = 1 / 2 * (1 + Real.sin θ + Real.cos θ)^2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33418; Apache-2.0

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