simp only [altFormula, mul_assoc, mul_eq_zero, sub_eq_zero]
x : ℝ
⊢ altFormula x = 0 ↔ x.cos ^ 2 = 1 / 2 ∨ (3 * x).cos = 0
x : ℝ
⊢ x.cos = 0 ∨ x.cos ^ 2 = 1 / 2 ∨ (3 * x).cos = 0 ↔ x.cos ^ 2 = 1 / 2 ∨ (3 * x).cos = 0