Can $\frac{\csc \alpha +\cos \alpha}{\cos \alpha – \tan \alpha – \sec \alpha}$ be simplified

Question

I am trying to simplify the following but I cannot.
$$
\frac{\csc \alpha +\cos \alpha}{\cos \alpha – \tan \alpha – \sec \alpha}
$$

Can it be simplified?

Edit

My last result is

$$
– \frac{\cos \alpha \left( 1 + \sin \alpha \cos \alpha\right)}
{\sin^2 \alpha \left(1+\sin \alpha\right)}
$$

I am wondering it might be a wrong question given by my student's teacher.

Answer 1

If you multiply the numerator and denominator of your last expression by $4(1-\sin\alpha)$ and use the identity $\sin2\alpha=2\sin\alpha\cos\alpha$, you can rewrite your result as $$(1-\csc\alpha)(2\csc2\alpha+1).$$ This reduces the original 24 symbols to 17.