In a right - angled triangle , it is given that A is an acute angle and `tan A=5/12`
`(cosA+sinA)/(cosA-sinA)`

Answer

To solve the problem, we need to find the value of the expression \((\cos A + \sin A) / (\cos A - \sin A)\) given that \(\tan A = \frac{5}{12}\).

### Step-by-Step Solution:

1. **Understanding the Triangle**:
- We know that \(\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{12}\).
- Let's denote the opposite side as 5 and the adjacent side as 12.

2. **Finding the Hypotenuse**:
- We can use the Pythagorean theorem to find the hypotenuse \(h\):
\[ h = \sqrt{(5^2) + (12^2)} = \sqrt{25 + 144} = \sqrt{169} = 13. \]

3. **Finding \(\sin A\) and \(\cos A\)**:
- Now we can find \(\sin A\) and \(\cos A\):
\[ \sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{5}{13}, \]
\[ \cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{13}. \]

4. **Substituting into the Expression**:
- Now substitute \(\sin A\) and \(\cos A\) into the expression:
\[ \frac{\cos A + \sin A}{\cos A - \sin A} = \frac{\frac{12}{13} + \frac{5}{13}}{\frac{12}{13} - \frac{5}{13}}. \]

5. **Simplifying the Numerator and Denominator**:
- The numerator becomes:
\[ \frac{12 + 5}{13} = \frac{17}{13}. \]
- The denominator becomes:
\[ \frac{12 - 5}{13} = \frac{7}{13}. \]

6. **Final Simplification**:
- Now, we can simplify the expression:
\[ \frac{\frac{17}{13}}{\frac{7}{13}} = \frac{17}{7}. \]

### Final Answer:
\[ \frac{\cos A + \sin A}{\cos A - \sin A} = \frac{17}{7}. \]