Theorems · Theorem · complex analysis
Complex.cos_add_cos
∀ (x y : ℂ), Complex.cos x + Complex.cos y = 2 * Complex.cos ((x + y) / 2) * Complex.cos ((x - y) / 2)
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_zeroproof · cited by 1,870
- one_ne_zeroproof · cited by 885
- div_oneproof · cited by 629
- Complex.cosstatement and proof · cited by 279
- Complex.sinproof · cited by 258
- Complex.cos_addproof · cited by 11
- Complex.cos_subproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.T_complex_cosproof · cited by 3
- Real.cos_add_cosproof · cited by 0