Theorems · Theorem · real analysis
Real.sin_nat_mul_pi_sub
∀ (x : ℝ) (n : ℕ), Real.sin (↑n * Real.pi - x) = -((-1) ^ n * Real.sin x)
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- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Real.pistatement and proof · cited by 1,774
- mul_negproof · cited by 590
- Real.sinstatement and proof · cited by 389
- Real.sin_negproof · cited by 34
- Real.sin_antiperiodicproof · cited by 14
- Function.Antiperiodic.nat_mul_sub_eqproof · cited by 2
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