If `sectheta=(13)/(12)`,then find the value of `cottheta`.

Answer

To solve the problem where \( \sec \theta = \frac{13}{12} \) and we need to find \( \cot \theta \), we can follow these steps:

### Step 1: Understand the definition of secant
The secant function is defined as:
\[ \sec \theta = \frac{\text{Hypotenuse}}{\text{Base}} \]
Given \( \sec \theta = \frac{13}{12} \), we can identify:
- Hypotenuse \( H = 13 \)
- Base \( B = 12 \)

### Step 2: Use the Pythagorean theorem to find the perpendicular
In a right triangle, the relationship between the sides is given by the Pythagorean theorem:
\[ H^2 = B^2 + P^2 \]
Substituting the known values:
\[ 13^2 = 12^2 + P^2 \]
Calculating the squares:
\[ 169 = 144 + P^2 \]
Now, isolate \( P^2 \):
\[ P^2 = 169 - 144 = 25 \]
Taking the square root gives:
\[ P = 5 \]

### Step 3: Calculate cotangent
The cotangent function is defined as:
\[ \cot \theta = \frac{\text{Base}}{\text{Perpendicular}} = \frac{B}{P} \]
Substituting the values we found:
\[ \cot \theta = \frac{12}{5} \]

### Final Answer
Thus, the value of \( \cot \theta \) is:
\[ \cot \theta = \frac{12}{5} \]

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