Theorems · Theorem · complex analysis
Complex.inv_one_add_tan_sq
∀ {x : ℂ}, Complex.cos x ≠ 0 → (1 + Complex.tan x ^ 2)⁻¹ = Complex.cos x ^ 2- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 148 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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- one_ne_zeroproof · cited by 885
- div_oneproof · cited by 629
- Complex.cosstatement and proof · cited by 279
- Complex.sinproof · cited by 258
- Complex.tanstatement · cited by 77
- div_powproof · cited by 66
- Complex.tan_eq_sin_div_cosproof · cited by 3
- Complex.cos_sq_add_sin_sqproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Real.inv_one_add_tan_sqproof · cited by 4
- Complex.cos_eq_two_mul_tan_half_div_one_sub_tan_half_sqproof · cited by 1
- Complex.sin_eq_two_mul_tan_half_div_one_add_tan_half_sqproof · cited by 1
- Complex.tan_sq_div_one_add_tan_sqproof · cited by 0