I need to provide a simplified version of this expression for a homework:
$ \frac{\cos^{3}x - 2\cdot\cos x + \sec x}{\cos x \cdot \sin^{2}x} $
Basically, there aren't restrictions. The simpler the final formula, the better. I've been trying to reduce this expression with the main idea of replacing trigonometric function with $\cos$ equivalents (as it appears more frequently, thus could be simplified), but this led me to nowhere.
$ \frac{\cos^{3}x - 2\cdot\cos x + \frac{1}{\cos x}}{\cos x (1 - \cos^{2}x)} $
I've also tried other substitutions with no success.
Any tip on direction to take from here are really appreciated. I see there is a lot of work to be done, and I know I haven't walked so much in direction to finishing it. The problem is that I don't have any idea to continue this.