Prove2Me

lean_workbook_plus_47397

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

Prove the identity: sinx(1−cosx)(1−cos2x)−sinx(1+cosx)(1−cos2x)=−2cosxsinxsin2x\frac{sinx(1-cosx)}{(1-cos^2x)} - \frac{sinx(1+cosx)}{(1-cos^2x)} = \frac{-2cosxsinx}{sin^2x} (using steps)

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_47397 :  ∀ x : ℝ, (sin x * (1 - cos x) / (1 - cos x ^ 2) - sin x * (1 + cos x) / (1 - cos x ^ 2) = -2 * cos x * sin x / sin x ^ 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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