The question was
Solve. $\sqrt{2}\cos x + \cot x = 0,\ x\in [-\pi, \pi]$
So she did
$\sqrt{2}\cos x + \frac{\cos x}{\sin x} = 0$ which is fine
But the next step confuses me. I understand where she went from this next step, but not how she got to it.
$\cos x(\sqrt{2} + \frac{1}{\sin x}) = 0$.
What I'm not understanding is, is how the $\sqrt{2}$ left the '$\cos x$' and joined the $\frac{1}{\sin x}$, and how the $\frac{\cos x}{\sin x}$ even became $\frac{1}{\sin x}$?
Any help would be great.