The given identity is
[tex]\cos (\pi-A)=-\cos A[/tex]
Step 1 is about the trigonometric identify of angle difference which states
[tex]\cos (\pi-A)=\cos \pi\cdot\cos A+\sin \pi\cdot\sin A[/tex]
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
[tex](-1)\cdot\cos A+0\cdot\sin A[/tex]
The second step is correct.
Steps 3 and 4 are about solving the products.
[tex](-1)\cdot\cos A+0\cdot\sin A=-\cos A+0[/tex]
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.
