State whether the following are true or false. Justify your Solution.
`sec=12/5`for some value of angle A.

Answer

To determine whether the statement "sec A = 12/5 for some value of angle A" is true or false, we can analyze the properties of the secant function.

### Step-by-Step Solution:

1. **Understanding the Secant Function**:
The secant function is defined as the reciprocal of the cosine function:
\[ \sec A = \frac{1}{\cos A} \]
Therefore, for sec A to exist, \(\cos A\) must not be zero.

2. **Range of the Secant Function**:
The range of the secant function is:
\[ \sec A \geq 1 \quad \text{or} \quad \sec A \leq -1 \]
This means that the secant function can take values greater than or equal to 1 or less than or equal to -1.

3. **Evaluating the Given Value**:
The given value is:
\[ \sec A = \frac{12}{5} = 2.4 \]
Since \(2.4\) is greater than \(1\), it falls within the acceptable range of the secant function.

4. **Finding the Cosine Value**:
To find if there exists an angle A such that \(\sec A = 2.4\), we can find \(\cos A\):
\[ \cos A = \frac{1}{\sec A} = \frac{1}{2.4} = \frac{5}{12} \]

5. **Existence of the Angle**:
The value \(\cos A = \frac{5}{12}\) is valid since the cosine function can take values between \(-1\) and \(1\). Therefore, there exists an angle A for which \(\cos A = \frac{5}{12}\).

6. **Conclusion**:
Since we have found a valid angle A such that \(\sec A = 2.4\), we conclude that the statement is **True**.

### Final Answer:
**True**: There exists an angle A such that \(\sec A = \frac{12}{5}\).