Theorems · Theorem · complex analysis
Real.sin_sq
∀ (x : ℝ), Real.sin x ^ 2 = 1 - Real.cos x ^ 2
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.cosstatement · cited by 424
- Real.sinstatement · cited by 389
- eq_sub_iff_add_eqproof · cited by 65
- Real.sin_sq_add_cos_sqproof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- Real.sin_sq_eq_half_subproof · cited by 3
- integral_sin_pow_odd_mul_cos_powproof · cited by 3
- integral_cos_pow_auxproof · cited by 1
- Real.abs_sin_eq_sqrt_one_sub_cos_sqproof · cited by 1
- Real.sin_sq_pi_over_two_powproof · cited by 1
- integral_sin_pow_even_mul_cos_pow_evenproof · cited by 1