Theorems · Theorem · complex analysis
Real.inv_one_add_tan_sq
∀ {x : ℝ}, Real.cos x ≠ 0 → (1 + Real.tan x ^ 2)⁻¹ = Real.cos x ^ 2- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Complex.ofRealproof · cited by 1,654
- Complex.reproof · cited by 882
- Real.cosstatement and proof · cited by 424
- Complex.cosproof · cited by 279
- Real.tanstatement and proof · cited by 100
- Complex.ofReal_addproof · cited by 94
- Complex.ofReal_powproof · cited by 81
- Complex.ofReal_invproof · cited by 62
- Complex.ofReal_cosproof · cited by 43
- Complex.ofReal_injproof · cited by 38
- Complex.ofReal_tanproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Real.inv_sqrt_one_add_tan_sqproof · cited by 2
- Real.cos_sq_arctanproof · cited by 1
- Real.tan_sq_div_one_add_tan_sqproof · cited by 1
- Real.cos_lt_one_div_sqrt_sq_add_oneproof · cited by 1