Answer:[tex]\begin{gathered} \text{Box 1: }\frac{1}{\cos x} \\ \text{Box 2: cosx} \\ \text{Box 3: cosx} \\ \text{Box 4: cosx} \end{gathered}[/tex]Explanations:The identity to verify is:[tex]\frac{\csc (x)-\cot (x)}{\sec (x)-1}=\text{ cot(x)}[/tex][tex]\begin{gathered} \frac{\csc(x)-\cot(x)}{\sec(x)-1}=\text{ }\frac{\frac{1}{\sin(x)}-\frac{\cos (x)}{\sin (x)}}{\frac{1}{\cos (x)}-1} \\ =\text{ }\frac{\frac{1}{\sin(x)}-\frac{\cos(x)}{\sin(x)}}{\frac{1}{\cos(x)}-1}\times\frac{\sin (x)\cos (x)_{}}{\sin (x)\cos (x)_{}} \\ =\frac{\cos (x)-\cos ^2(x)}{\sin (x)-\sin (x)\cos (x)} \\ =\frac{\cos (x)(1\text{ - cos(x))}}{\sin (x)(1\text{ - cos(x))}} \\ =\frac{\cos (x)}{\sin (x)} \\ =\text{ cot(x)} \end{gathered}[/tex]
