Verify the Identity (1 − cos(𝛽))(1 + cos(𝛽)) = 1 /csc^2(𝛽)

Question

Verify the identity (1 − cos(𝛽))(1 + cos(𝛽)) = 1 /csc^2(𝛽)

It wants me to verify by expanding the right side

I got to (1-cos(𝛽))(1+cos(𝛽))=1-(cos^2(𝛽))

Answer 1

1/csc²(B)=sin²(B)=1-cos²(B)