Theorems · Theorem · complex analysis
Real.sin_mul_sum_cos
∀ (n : ℕ) (a b : ℝ),
Real.sin (a / 2) * ∑ i ∈ Finset.range n, Real.cos (a * ↑i + b) =
Real.sin (↑n * a / 2) * Real.cos ((↑n - 1) * a / 2 + b)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- Complexproof · cited by 5,565
- Finset.sumstatement and proof · cited by 5,195
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- Complex.ofRealproof · cited by 1,654
- Finset.rangestatement and proof · cited by 1,341
- Complex.reproof · cited by 882
- Real.cosstatement and proof · cited by 424
- Real.sinstatement and proof · cited by 389
- Complex.cosproof · cited by 279
- Complex.sinproof · cited by 258
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