<s>[INST] Transforming the equation $\cot x -\cos x = 0$ into the form $\cos x(1- \sin x) = 0$ 
I am required to write the equation $$\cot x - \cos x = 0$$ 
  in the form 
  $$\cos x(1 - \sin x) = 0$$ 

What I reached is as follows,
\begin{align}
\cot x & = \frac{\cos x}{\sin x}\\[4pt]
\frac{\cos x}{\sin x} - \cos x & = 0\\[4pt]
\cos x\left(\frac{1}{\sin x} - 1\right) & = 0\\[4pt]
\cos x\left(\frac{1}{\sin x} - \frac{\sin x}{\sin x}\right) & = 0
\end{align}
How can I rewrite in the above format?
 [/INST] $$
\cot(X)-\cos(X) =  0 \implies \frac{\cos X}{\sin X} - \cos X = 0 \implies \cos X\bigg(\frac{1}{\sin X} - 1\bigg) = 0
$$
$$
\implies \frac{\cos X(1 - \sin X)}{\sin X} = 0 \implies \cos X(1 - \sin X) = 0 \cdot \sin X = 0
$$
This applies when $\sin X \neq 0$. If it is zero, then $\cot X = \infty$ so the equation is not satisfied.
</s>