Theorems · Theorem · complex analysis
Complex.cos_two_mul
∀ (x : ℂ), Complex.cos (2 * x) = 2 * Complex.cos x ^ 2 - 1
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Complex.cosstatement and proof · cited by 279
- two_mulproof · cited by 232
- eq_sub_iff_add_eqproof · cited by 65
- sub_addproof · cited by 51
- sub_add_eq_add_subproof · cited by 29
- Complex.sin_sq_add_cos_sqproof · cited by 11
- Complex.cos_two_mul'proof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Real.cos_two_mulproof · cited by 4
- Complex.cos_sqproof · cited by 1
- Complex.sin_three_mulproof · cited by 1