Find the value of :
`sin30^(@)cos30^(@)`

Answer

To find the value of \( \sin 30^\circ \cos 30^\circ \), we can follow these steps:

### Step 1: Identify the values of \( \sin 30^\circ \) and \( \cos 30^\circ \)
From the standard trigonometric ratios, we know:
- \( \sin 30^\circ = \frac{1}{2} \)
- \( \cos 30^\circ = \frac{\sqrt{3}}{2} \)

### Step 2: Substitute the values into the expression
Now, we substitute these values into the expression \( \sin 30^\circ \cos 30^\circ \):
\[ \sin 30^\circ \cos 30^\circ = \left(\frac{1}{2}\right) \left(\frac{\sqrt{3}}{2}\right) \]

### Step 3: Multiply the fractions
Now, we multiply the two fractions:
\[ \sin 30^\circ \cos 30^\circ = \frac{1 \cdot \sqrt{3}}{2 \cdot 2} = \frac{\sqrt{3}}{4} \]

### Final Answer
Thus, the value of \( \sin 30^\circ \cos 30^\circ \) is:
\[ \frac{\sqrt{3}}{4} \]

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