1. **Simplify** $\csc^2 x \tan^2 x \cos x$. Recall that $\csc x = \frac{1}{\sin x}$ and $\tan x = \frac{\sin x}{\cos x}$. $$\csc^2 x \tan^2 x \cos x = \left(\frac{1}{\sin^2 x}\right) \left(\frac{\sin^2 x}{\cos^2 x}\right) \cos x$$ 2. Cancel $\sin^2 x$: $$= \frac{\cancel{1}}{\cancel{\sin^2 x}} \cdot \frac{\cancel{\sin^2 x}}{\cos^2 x} \cdot \cos x = \frac{\cos x}{\cos^2 x}$$ 3. Simplify the fraction: $$= \frac{\cancel{\cos x}}{\cos^2 x} = \frac{1}{\cos x} = \sec x$$ **Final answer:** $\sec x$