A student guesses three formulas for cos 2a: 2 cos² a - 1, 1 - 2 sin² a and 2 cos a…

Step 1. The test. The program finds True for the first two and False for the third.

Step 2. By hand. At $a = 90^\circ$, $\cos 2a = \cos 180^\circ = -1$, but $2\cos a = 0$. One counterexample proves the third formula false.

Step 3. The first two. Both follow from $\cos 2a = \cos^2 a - \sin^2 a$ and $\sin^2 a + \cos^2 a = 1$.