Theorems · Theorem · real analysis
Real.cos_nat_mul_two_pi_sub_pi
∀ (n : ℕ), Real.cos (↑n * (2 * Real.pi) - Real.pi) = -1
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- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Real.pistatement and proof · cited by 1,774
- Real.cosstatement and proof · cited by 424
- Real.cos_zeroproof · cited by 38
- Real.cos_antiperiodicproof · cited by 16
- Real.cos_periodicproof · cited by 16
- Function.Periodic.nat_mulproof · cited by 15
- Function.Periodic.sub_antiperiod_eqproof · cited by 4
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