If ` 2 sin 3 theta = 1` , then the value of `theta` is :

Options

A. `30^(@)`
B. `20^(@)`
C. `10^(@)`
D. `45^(@)`

Answer

To solve the equation \( 2 \sin 3\theta = 1 \), we can follow these steps:

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ 2 \sin 3\theta = 1 \]

2. **Isolate \(\sin 3\theta\):**
Divide both sides of the equation by 2:
\[ \sin 3\theta = \frac{1}{2} \]

3. **Determine the angle whose sine is \(\frac{1}{2}\):**
We know that:
\[ \sin 30^\circ = \frac{1}{2} \]
Therefore, we can set:
\[ 3\theta = 30^\circ \]

4. **Solve for \(\theta\):**
Divide both sides by 3:
\[ \theta = \frac{30^\circ}{3} = 10^\circ \]

5. **Conclusion:**
The value of \(\theta\) is:
\[ \theta = 10^\circ \]