Given : `cos A=5/13` evaluate :
`(sinA-cotA)/(2 tanA)`

Answer

To solve the problem given that \( \cos A = \frac{5}{13} \), we need to evaluate the expression \( \frac{\sin A - \cot A}{2 \tan A} \).

### Step 1: Determine the sides of the triangle
Since \( \cos A = \frac{5}{13} \), we can interpret this in a right triangle where:
- The base (adjacent side) is 5,
- The hypotenuse is 13.

Using the Pythagorean theorem, we can find the length of the perpendicular (opposite side):
\[ \text{Hypotenuse}^2 = \text{Perpendicular}^2 + \text{Base}^2 \]
\[ 13^2 = \text{Perpendicular}^2 + 5^2 \]
\[ 169 = \text{Perpendicular}^2 + 25 \]
\[ \text{Perpendicular}^2 = 169 - 25 = 144 \]
\[ \text{Perpendicular} = \sqrt{144} = 12 \]

### Step 2: Calculate \( \sin A \), \( \cot A \), and \( \tan A \)
Now we can find:
- \( \sin A = \frac{\text{Perpendicular}}{\text{Hypotenuse}} = \frac{12}{13} \)
- \( \cot A = \frac{\text{Base}}{\text{Perpendicular}} = \frac{5}{12} \)
- \( \tan A = \frac{\text{Perpendicular}}{\text{Base}} = \frac{12}{5} \)

### Step 3: Substitute into the expression
Now substitute these values into the expression \( \frac{\sin A - \cot A}{2 \tan A} \):
\[ \frac{\sin A - \cot A}{2 \tan A} = \frac{\frac{12}{13} - \frac{5}{12}}{2 \cdot \frac{12}{5}} \]

### Step 4: Simplify the numerator
To simplify the numerator \( \frac{12}{13} - \frac{5}{12} \), we need a common denominator:
- The common denominator is \( 12 \times 13 = 156 \).

Now convert each fraction:
\[ \frac{12}{13} = \frac{12 \times 12}{13 \times 12} = \frac{144}{156} \]
\[ \frac{5}{12} = \frac{5 \times 13}{12 \times 13} = \frac{65}{156} \]

Now subtract:
\[ \frac{144}{156} - \frac{65}{156} = \frac{144 - 65}{156} = \frac{79}{156} \]

### Step 5: Simplify the denominator
Now calculate the denominator \( 2 \tan A \):
\[ 2 \tan A = 2 \cdot \frac{12}{5} = \frac{24}{5} \]

### Step 6: Combine the results
Now we have:
\[ \frac{\frac{79}{156}}{\frac{24}{5}} = \frac{79}{156} \cdot \frac{5}{24} = \frac{79 \cdot 5}{156 \cdot 24} = \frac{395}{3744} \]

### Final Answer
Thus, the value of \( \frac{\sin A - \cot A}{2 \tan A} \) is:
\[ \frac{395}{3744} \]