Theorems · Theorem · real analysis
Real.cos_nat_mul_pi_sub
∀ (x : ℝ) (n : ℕ), Real.cos (↑n * Real.pi - x) = (-1) ^ n * Real.cos x
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 1,774
- Real.cosstatement · cited by 424
- Real.cos_negproof · cited by 27
- Real.cos_antiperiodicproof · cited by 16
- Function.Antiperiodic.nat_mul_sub_eqproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- HurwitzZeta.hurwitzZetaOdd_neg_two_mul_natproof · cited by 0
- HurwitzZeta.hurwitzZetaEven_one_sub_two_mul_natproof · cited by 0