Theorems · Theorem · real analysis
Real.cos_arctan
∀ (x : ℝ), Real.cos (Real.arctan x) = 1 / √(1 + x ^ 2)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 205 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.
- Realstatement and proof · cited by 25,697
- one_divproof · cited by 624
- Real.sqrtstatement and proof · cited by 545
- Real.cosstatement and proof · cited by 424
- Real.arctanstatement and proof · cited by 111
- Real.tan_arctanproof · cited by 11
- Real.cos_arctan_posproof · cited by 6
- Real.inv_sqrt_one_add_tan_sqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radiusproof · cited by 2