Simplify the given trigonometric expression: $\frac{\cot x}{\cos x}$

Step 1 ：Given the trigonometric expression: \(\frac{\cot x}{\cos x}\)

Step 2 ：The cotangent of x, \(\cot(x)\), can be expressed as the reciprocal of the tangent of x, \(\tan(x)\). Therefore, \(\cot(x) = \frac{1}{\tan(x)}\)

Step 3 ：The tangent of x, \(\tan(x)\), can be expressed as the sine of x, \(\sin(x)\), divided by the cosine of x, \(\cos(x)\). Therefore, \(\tan(x) = \frac{\sin(x)}{\cos(x)}\)

Step 4 ：Substituting these expressions into the original expression, we get \(\frac{1}{(\sin(x)/\cos(x))}/\cos(x) = \frac{1}{\sin(x)\cdot \cos(x)} = \frac{\cos(x)}{\sin(x)}\)

Step 5 ：The simplified expression is \(\frac{1}{\sin(x)}\), which is the reciprocal of the sine of x, also known as the cosecant of x, \(\csc(x)\)

Step 6 ：Final Answer: \(\boxed{\csc x}\)