InnerProductGeometry.tan_angle_add_of_inner_eq_zero
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {x y : V},
inner ℝ x y = 0 → Real.tan (InnerProductGeometry.angle x (x + y)) = ‖y‖ / ‖x‖The tangent of an angle in a right-angled triangle as a ratio of sides.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- zero_addproof · cited by 2,366
- Inner.innerstatement and proof · cited by 1,089
- norm_zeroproof · cited by 366
- div_zeroproof · cited by 251
- InnerProductGeometry.anglestatement and proof · cited by 170
- Real.tanstatement and proof · cited by 100
- InnerProductGeometry.angle_zero_leftproof · cited by 14
- Real.tan_arctanproof · cited by 11
Cited by5
Results whose statement or proof uses this declaration.
- InnerProductGeometry.norm_div_tan_angle_add_of_inner_eq_zeroproof · cited by 3
- InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zeroproof · cited by 3
- EuclideanGeometry.tan_angle_of_angle_eq_pi_div_twoproof · cited by 2
- Orientation.tan_oangle_add_right_of_oangle_eq_pi_div_twoproof · cited by 1
- InnerProductGeometry.tan_angle_sub_of_inner_eq_zeroproof · cited by 1