Help with L'Hospital's Rule question

Hey guys,

I was just wondering if you could help me out with a question. I think I've wittled it down enough but I'm having troubles simplifying it and I'm not sure if I've done one step right.

Here's the question:

Evaluate the limit.

http://www.webassign.net/cgi-bin/sym...sin%288%20x%29

This is what I have gotten so far:

lim x --> 0 = sin(8x) / -tan(4x)^-2 (because, 1/1/cot(4x) = tan(4x)^-1, and the derivative of that is what I have written)

Took the deriv. again because I get 0/0

lim x --> 0 = 8cos(8x) / -4sec^2(4x)^-2 << this is the step I'm not sure about, with sec. I don't think that's the right derivative.

Any help's appreciated. Thanks!