To evaluate the integral 

\[
\int \frac{\cos x}{\sin x} \, dx,
\]

we can simplify the integrand using a trigonometric identity. Notice that:

\[
\frac{\cos x}{\sin x} = \cot x.
\]

Therefore, the integral becomes:

\[
\int \cot x \, dx.
\]

### Step-by-Step Solution

To integrate \(\cot x\), we use the fact that:

\[
\cot x = \frac{\cos x}{\sin x} \implies \int \cot x \, dx = \int \frac{\cos x}{\sin x} \, dx.
\]

Now, we know that the integral of \(\cot x\) is:

\[
\int \cot x \, dx = \ln|\sin x| + C,
\]

where \(C\) is the constant of integration.

### Final Answer

Thus, the integral evaluates to:

\[
\int \frac{\cos x}{\sin x} \, dx = \ln|\sin x| + C.
\]

Would you like more details, or do you have any further questions?

### Related Questions

1. How do you integrate \(\int \csc x \, dx\)?
2. What is the integral of \(\int \tan x \, dx\)?
3. Can you solve the integral \(\int \sec^2 x \, dx\)?
4. How do you solve integrals involving trigonometric identities?
5. What is the integral of a trigonometric function like \(\sin(x)\) or \(\cos(x)\)?

**Tip:** When integrating trigonometric functions, look for standard forms or identities to simplify the problem.

Learn how to evaluate the integral ∫cos(x)dx/sin(x) with a step-by-step solution. This problem involves trigonometric integrals and integration techniques, using the formula ∫cot(x)dx = ln|sin(x)| + C. Suitable for students in Grades 11-12.

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