1. ## Identity troubles...

I'm reviewing for a test and I came across this problem:

Simplify: sec(x)cot(x)sin(2x)

I've been trying different things for about an hour, but I can't figure out how to get 2cos(x) which is the answer in the back of the book. Could anyone help me get started?

I'm reviewing for a test and I came across this problem:

Simplify: sec(x)cot(x)sin(2x)

I've been trying different things for about an hour, but I can't figure out how to get 2cos(x) which is the answer in the back of the book. Could anyone help me get started?
It's actually a one step problem

$\displaystyle \sec x \cot x \sin 2x = \frac {1}{\cos x} \cdot \frac {\cos x}{ \sin x } \cdot 2 \sin x \cos x$ $\displaystyle = 2 \cos x$

what things were you trying?

3. Thanks. I found the problem. In my first attempt I made a simple mistake and incorrectly derived that...

$\displaystyle \frac {1}{\cos x} \cdot \frac {\cos x}{\sin x} = \sin x$ and not $\displaystyle \frac {1}{\sin x}$

Leading to overcomplication of the problem and frustration in future attempts. Seeing it on the computer made it clear compared to my rather inconsistent handwriting.