(sec(x)/(sin(x))-(sin(x)/(cos(x))

I believe the answer is (1-sin(x))/(sin(x)cos(x)).

Whoops. Just double checked my math. Made an error. Here's the REAL answer:

Sec(x) = 1/cos(x), so ((1/cos(x))/sin(x))-(sin(x)/cos(x))

Then multiply the first term by cos(x), and get (1/sin(x)*cos(x))-(sin(x)/(cos(x))

Multiply the second term by sin(x) -> (1/sin(x)*cos(x))-(sin^2(x)/cos(x)*sin(x))

Since you now have common denominators, you can subtract and get (1-sin^2(x))/(sin(x)*cos(x))

1-sin^2(x) = cos^2(x), so cos^2(x)/(sin(x)*cos(x))

Then simplify to cos(x)/(sin(x)), then to cot(x).