The given identity is

Step 1 is about the trigonometric identify of angle difference which states

So, the first step is wrong since they used subtraction instead of addition.
Step 2 is about solving each trigonometric function of pi. We know that the cosine of pi is -1, and the sine of pi is 0. So, we have

The second step is correct.
Steps 3 and 4 are about solving the products.

Steps 3 and 4 are correct.
Step 5 is also correct since the zero doesn't change the cosine function.
Therefore, step 1 is the mistake in the given demonstration.