Theorems · Theorem · real analysis
Real.arctan_eq_arcsin
∀ (x : ℝ), Real.arctan x = Real.arcsin (x / √(1 + x ^ 2))
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 206 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
- Real.sqrtstatement · cited by 545
- Real.arcsinstatement · cited by 125
- Real.arctanstatement · cited by 111
- Set.mem_Icc_of_Iooproof · cited by 9
- Real.arctan_mem_Iooproof · cited by 7
- Real.arcsin_eq_of_sin_eqproof · cited by 6
- Real.sin_arctanproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Real.arctan_zeroproof · cited by 17
- Real.arctan_negproof · cited by 6
- InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zeroproof · cited by 4
- Real.arcsin_eq_arctanproof · cited by 0
- Real.arctan_eq_arccosproof · cited by 0