Theorems · Theorem · complex analysis
Complex.sin_sq_add_cos_sq
∀ (x : ℂ), Complex.sin x ^ 2 + Complex.cos x ^ 2 = 1
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 146 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.
- Complexstatement and proof · cited by 5,565
- add_commproof · cited by 1,535
- Complex.Iproof · cited by 866
- Complex.cosstatement and proof · cited by 279
- sub_neg_eq_addproof · cited by 264
- Complex.sinstatement and proof · cited by 258
- mul_powproof · cited by 220
- Complex.sinhproof · cited by 113
- Complex.I_sqproof · cited by 40
- mul_neg_oneproof · cited by 30
- Complex.cosh_mul_Iproof · cited by 11
- Complex.sinh_mul_Iproof · cited by 10
Cited by11
Results whose statement or proof uses this declaration.
- Real.sin_sq_add_cos_sqproof · cited by 12
- Complex.cos_two_mulproof · cited by 3
- Complex.tendsto_norm_tan_of_cos_eq_zeroproof · cited by 3
- integral_gaussian_sq_complexproof · cited by 2
- Complex.hasStrictDerivAt_tanproof · cited by 2
- Complex.cos_sq'proof · cited by 1
- Complex.cos_sq_add_sin_sqproof · cited by 1
- Complex.sin_sqproof · cited by 1
- Complex.one_add_tan_sq_mul_cos_sq_eq_oneproof · cited by 1
- Complex.cos_eq_zero_iff_sin_eqproof · cited by 0
- Complex.sin_eq_zero_iff_cos_eqproof · cited by 0