Verify the identity. (Simplify at each step.)

Question

I am a bit confused because every time I put in this answer for the blank fill-in it keeps saying it is wrong but shouldn't the answer for the it be cos²(𝛼)?

(1 + cos 𝛼)(1 − cos 𝛼) = sin² 𝛼

(1 + cos 𝛼)(1 − cos 𝛼) = 1 − (cos²𝛼) = sin²𝛼 (Fill-in answer is bolded and underlined)

Answer 1

(1 + cos α)(1 - cos α)

1 + cos α - cos α - cos² α

1 - cos² α

sin² α