use the identity (a+b)(a-b) = a^2 - b^2 with {(sec x)-1}{ (sec x +1) } to get

sec^2(x) - 1

we can now write expression as

{sec^2(x) -1} * cot (x)

and use the trig identity sec^2(x) - 1 = tan^2(x) to get expression as

tan^2(x)*cot(x) = tan^2(x) * {1/tan(x)} = tan(x)