You seem to be on the right track. I would start with defining , and begin with , then take the derivative and see if you recognize it.
Can I get help on the following HW question:
If X is a standard Cauchy Random Variable then 1/X is also a standard Cauchy Random Variable. How can it be proved?
Is it correct to say that: P(1/X<x) = P(X>1/x) = 1 - P(X<1/x) for x>0?
What about if x<0