Theorems · Theorem · real analysis
Real.abs_sin_half
∀ (x : ℝ), |Real.sin (x / 2)| = √((1 - Real.cos x) / 2)
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- absstatement · cited by 1,814
- Real.sqrtstatement and proof · cited by 545
- Real.cosstatement and proof · cited by 424
- Real.sinstatement and proof · cited by 389
- two_mulproof · cited by 232
- add_halvesproof · cited by 78
- sub_divproof · cited by 37
- Real.sqrt_sq_eq_absproof · cited by 13
- Real.sin_sq_eq_half_subproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Real.sin_half_eq_neg_sqrtproof · cited by 1
- Real.sin_half_eq_sqrtproof · cited by 1
- Complex.abs_cpow_inv_two_improof · cited by 0