$\lim _{x \rightarrow \frac{3 \pi}{2}} \frac{\cos x}{\sin x-1}=$

Step 1 ：We are given the limit function \(\lim _{x \rightarrow \frac{3 \pi}{2}} \frac{\cos x}{\sin x-1}\)

Step 2 ：To find the limit of a function as x approaches a certain value, we substitute the value of x into the function.

Step 3 ：Substituting \(\frac{3 \pi}{2}\) into the function, we get \(\frac{\cos(\frac{3 \pi}{2})}{\sin(\frac{3 \pi}{2})-1}\)

Step 4 ：This simplifies to \(\frac{0}{0-1}\), or 0.

Step 5 ：Therefore, the limit of the function as x approaches \(\frac{3 \pi}{2}\) is 0.

Step 6 ：Final Answer: \(\boxed{0}\)