Prove the identity

I think this should be written as (cot²B - cos²B)/(csc²B - 1) 

$$$$\frac{\cot^2B-\cos^2B}{\csc^2B-1}=\frac{\frac{\cos^2B}{\sin^2B}-\cos^2B}{\frac{1}{sin^2B}-1}$$\\
$$=\frac{\cos^2B-\sin^2B\cos^2B}{1-\sin^2B}$$\\
$$=\frac{\cos^2B(1-\sin^2B)}{1-\sin^2B}$$\\
$$=\cos^2B$$