We are given the following expression:
[tex]\sec x\cot x[/tex]In order to simplify this expression we will use the following relationship:
[tex]\sec x=\frac{1}{\cos x}[/tex]Replacing we get:
[tex]\sec x\cot x=(\frac{1}{\cos x})(\cot x)[/tex]Now we will use the following relationship:
[tex]\cot x=\frac{\cos x}{\sin x}[/tex]Replacing we get:
[tex](\frac{1}{\cos x})(\cot x)=(\frac{1}{\cos x})(\frac{\cos x}{\sin x})[/tex]Now we cancel out the cosines of x:
[tex](\frac{1}{\cos x})(\frac{\cos x}{\sin x})=\frac{1}{\sin x}[/tex]And this expression is equivalent to cosecant of "x", therefore:
[tex]\sec x\cot x=\csc x[/tex]