Theorems · Theorem · complex analysis
Complex.tan_sub
∀ {x y : ℂ},
(((∀ (k : ℤ), x ≠ (2 * ↑k + 1) * ↑Real.pi / 2) ∧ ∀ (l : ℤ), y ≠ (2 * ↑l + 1) * ↑Real.pi / 2) ∨
(∃ k, x = (2 * ↑k + 1) * ↑Real.pi / 2) ∧ ∃ l, y = (2 * ↑l + 1) * ↑Real.pi / 2) →
Complex.tan (x - y) = (Complex.tan x - Complex.tan y) / (1 + Complex.tan x * Complex.tan y)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Nat.cast_oneproof · cited by 2,501
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Int.cast_oneproof · cited by 371
- Int.cast_negproof · cited by 224
- Int.cast_subproof · cited by 78
- Complex.tanstatement and proof · cited by 77
- neg_eq_iff_eq_negproof · cited by 60
- Complex.tan_negproof · cited by 5
- Complex.tan_addproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Real.tan_subproof · cited by 1
- Complex.tan_sub'proof · cited by 0