Add or subtract as indicated, and then simplify as much as possible. Leave your answer in terms of sines and cosines only. \( \cos (x)+\frac{1}{\sin (x)}=\square \)

To combine the terms, first rewrite everything in terms of sine and cosine. The term \(\frac{1}{\sin(x)}\) can be expressed using the identity \(\sec(x) = \frac{1}{\cos(x)}\) as \(\frac{\cos(x)}{\sin(x)\cos(x)}\). So, we have: \[\cos(x) + \frac{1}{\sin(x)} = \cos(x) + \frac{\cos(x)}{\sin(x)\cos(x)} = \frac{\cos^2(x)}{\sin(x)\cos(x)} + \frac{1}{\sin(x)}\] Combine the fractions: \[= \frac{\cos^2(x) + \sin(x)}{\sin(x)\cos(x)}\] Now, simplify this expression as necessary. However, it's best to leave it in this form for clarity in terms of sine and cosine. So, the final answer in terms of sines and cosines is: \[\frac{\cos^2(x) + 1}{\sin(x)}\]