Theorems · Theorem · complex analysis
Real.sin_sq_add_cos_sq
∀ (x : ℝ), Real.sin x ^ 2 + Real.cos x ^ 2 = 1
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 151 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
- Complex.ofRealproof · cited by 1,654
- Real.cosstatement and proof · cited by 424
- Real.sinstatement and proof · cited by 389
- Complex.ofReal_addproof · cited by 94
- Complex.ofReal_powproof · cited by 81
- Complex.ofReal_cosproof · cited by 43
- Complex.ofReal_sinproof · cited by 40
- Complex.ofReal_injectiveproof · cited by 23
- Complex.sin_sq_add_cos_sqproof · cited by 11
Cited by12
Results whose statement or proof uses this declaration.
- Real.sin_pi_div_twoproof · cited by 29
- Real.sin_sqproof · cited by 6
- Complex.norm_cos_add_sin_mul_Iproof · cited by 6
- Real.cos_sq_add_sin_sqproof · cited by 5
- Real.cos_sq'proof · cited by 4
- Real.cos_arcsinproof · cited by 4
- Real.sin_eq_zero_iff_cos_eqproof · cited by 2
- Real.sin_sq_le_oneproof · cited by 2
- circleAverage_log_norm_sub_const₁proof · cited by 1
- Real.cos_sq_le_oneproof · cited by 1
- InnerProductGeometry.norm_ofLp_crossProductproof · cited by 1
- Real.cos_eq_zero_iff_sin_eqproof · cited by 0