Dev tries the rule sin(a + b) = sin a + sin b with a = 20° and b = 50°…

An identity holds for every angle. np.allclose(left, right) tests arrays; np.max(np.abs(left - right)) is the worst miss. One counterexample proves an identity false. Avoid angles where $\cos a = 0$ for $\tan$ and $\sec$. Random angles from rng.uniform(0, 2 * np.pi, n) test an identity everywhere.