The problem is to find:
$\lim\limits_{x \to 0}\ \dfrac{\sin(\cos(x))}{\sec(x)}$
I rewrite the equation as follows:
$\lim\limits_{x \to 0}\ \dfrac{\sin(\cos(x))}{\dfrac{1}{\cos(x)}}$
And multiply by $\dfrac{\cos(x)}{\cos(x)}$, producing:
$\lim\limits_{x \to 0}\ \dfrac{\cos(x)*\sin(\cos(x))}{\dfrac{\cos(x)}{\cos(x)}}$
And rewrite as:
$\lim\limits_{x \to 0}\ \cos^2(x)\ \dfrac{\sin(\cos(x))}{\cos(x)}$
Which then becomes:
$\lim\limits_{x \to 0}\ \cos^2(x) * 1$
Which becomes 1. However, the answer is apparently $\sin(1)$. What am I doing wrong?
Edit: I found a different way to solve this, but I'm still not sure what I did wrong originally.