To simplify the expression we fist need to express each trigonometric function in terms of sines and cosines; to do this we need to remember that:
[tex]\begin{gathered} \sec x=\frac{1}{\cos x} \\ \csc x=\frac{1}{\sin x} \end{gathered}[/tex]
With this in mind we have:
[tex]\begin{gathered} \frac{\csc x}{\sec x}=\frac{\frac{1}{\sin x}}{\frac{1}{\cos x}} \\ =\frac{\cos x}{\sin x} \end{gathered}[/tex]
Finally we need to remember that:
[tex]\cot x=\frac{\cos x}{\sin x}[/tex]
Therefore, we have that:
[tex]\frac{\csc x}{\sec x}=\cot x[/tex]
