Question

(_____)^2= (cscx-1)(cscx+1)

Answer 1

$(csc(x)-1)(csc(x)+1)=csc^2(x)-1=cot^2(x)$

We know that $csc^2(x)-1=cot^2(x)$ because of the Pythagorean trig identity $1+cot^2(x)=csc^2(x)$.