Value of `Sin15^(@).cos15^(@)` is:

Options

A. `1`
B. `1//2`
C. `1//4`
D. `(sqrt3)/(2)`

Explanation

To find the value of \( \sin 15^\circ \cdot \cos 15^\circ \), we can use a trigonometric identity.

### Step-by-Step Solution:

1. **Recall the Double Angle Identity**:
We know that:
\[ \sin 2x = 2 \sin x \cos x \]
This means that \( \sin x \cdot \cos x = \frac{1}{2} \sin 2x \).

2. **Set \( x = 15^\circ \)**:
By substituting \( x = 15^\circ \) into the identity, we have:
\[ \sin 30^\circ = 2 \sin 15^\circ \cos 15^\circ \]

3. **Calculate \( \sin 30^\circ \)**:
We know that:
\[ \sin 30^\circ = \frac{1}{2} \]

4. **Substitute \( \sin 30^\circ \) into the equation**:
Now we can write:
\[ \frac{1}{2} = 2 \sin 15^\circ \cos 15^\circ \]

5. **Solve for \( \sin 15^\circ \cdot \cos 15^\circ \)**:
Dividing both sides by 2 gives:
\[ \sin 15^\circ \cos 15^\circ = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} \]

### Final Answer:
Thus, the value of \( \sin 15^\circ \cdot \cos 15^\circ \) is \( \frac{1}{4} \).