Given : ` 4 cot A = 3 ` , find :
sec A

Answer

To solve the problem, we will follow these steps:

### Step 1: Start with the given equation
We are given that:
\[ 4 \cot A = 3 \]

### Step 2: Solve for cot A
To find cot A, we will divide both sides of the equation by 4:
\[ \cot A = \frac{3}{4} \]

### Step 3: Understand cotangent in terms of a right triangle
Recall that:
\[ \cot A = \frac{\text{base}}{\text{perpendicular}} \]
From the equation \( \cot A = \frac{3}{4} \), we can interpret this as:
- Base = 3
- Perpendicular = 4

### Step 4: Use the Pythagorean theorem to find the hypotenuse
We can find the hypotenuse (h) using the Pythagorean theorem:
\[ h = \sqrt{(\text{base})^2 + (\text{perpendicular})^2} \]
Substituting the values:
\[ h = \sqrt{3^2 + 4^2} \]
\[ h = \sqrt{9 + 16} \]
\[ h = \sqrt{25} \]
\[ h = 5 \]

### Step 5: Find secant A
Secant (sec A) is defined as:
\[ \sec A = \frac{\text{hypotenuse}}{\text{base}} \]
Substituting the values we have:
\[ \sec A = \frac{5}{3} \]

### Final Answer
Thus, the value of sec A is:
\[ \sec A = \frac{5}{3} \]

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