`sin 60^(@)cos30^(@)` is equal to:

Options

A. 1
B. `(2sqrt3)/(4)`
C. `(4)/(3)`
D. `(3)/(4)`

Answer

To solve the expression \( \sin 60^\circ \cos 30^\circ \), we will follow these steps:

### Step 1: Find the value of \( \sin 60^\circ \)
We know that:
\[ \sin 60^\circ = \frac{\sqrt{3}}{2} \]

### Step 2: Find the value of \( \cos 30^\circ \)
We also know that:
\[ \cos 30^\circ = \frac{\sqrt{3}}{2} \]

### Step 3: Multiply the values obtained in Steps 1 and 2
Now we can substitute these values into the expression:
\[ \sin 60^\circ \cos 30^\circ = \left(\frac{\sqrt{3}}{2}\right) \left(\frac{\sqrt{3}}{2}\right) \]

### Step 4: Simplify the multiplication
Calculating the multiplication:
\[ \sin 60^\circ \cos 30^\circ = \frac{\sqrt{3} \cdot \sqrt{3}}{2 \cdot 2} = \frac{3}{4} \]

### Final Answer
Thus, the value of \( \sin 60^\circ \cos 30^\circ \) is:
\[ \frac{3}{4} \]