If `sin 2A = (1)/(2)`, then `(1)/("2 sin A cos A")=`

Options

A. 1
B. `(3)/(2)`
C. 2
D. 3

Explanation

To solve the problem, we start with the given equation:

1. **Given:** \( \sin 2A = \frac{1}{2} \)

2. **Using the double angle formula for sine:**
\[ \sin 2A = 2 \sin A \cos A \]
Therefore, we can write:
\[ 2 \sin A \cos A = \frac{1}{2} \]

3. **Now, we need to find \( \frac{1}{2 \sin A \cos A} \):**
From the equation \( 2 \sin A \cos A = \frac{1}{2} \), we can rearrange it to find \( \sin A \cos A \):
\[ \sin A \cos A = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} \]

4. **Substituting back into our expression:**
\[ \frac{1}{2 \sin A \cos A} = \frac{1}{2 \cdot \frac{1}{4}} = \frac{1}{\frac{1}{2}} = 2 \]

5. **Conclusion:**
Therefore, the value of \( \frac{1}{2 \sin A \cos A} \) is \( 2 \).

Thus, the answer is \( 2 \), which corresponds to option C.