Step-by-step explanation:
The first four lines are correct. Your mistake is after you get to this part:
lim(n→0) (2 sin²(n/2) / n)
In the fifth line, it looks like you try to write this limit as:
2 lim(n→0) ¼ (sin (n/2) / (n/2))²
But these are not the same. You're introducing another n in the denominator.
Here's what you should do instead:
lim(n→0) (2 sin²(n/2) / n)
lim(n→0) (sin²(n/2) / (n/2))
lim(n→0) (sin (n/2) / (n/2)) × lim(n→0) (sin (n/2))
1 × 0
0
Now when you plug this in, you get (0 + 1) / (0 − 1) = -1.
