Find the value of `sin60^(@)cos30^(@)+cos60^(@)sin30^(@)`.

Answer

To find the value of \( \sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ \), we can follow these steps:

### Step 1: Identify the trigonometric values
We need to use the known values of the trigonometric functions:
- \( \sin 60^\circ = \frac{\sqrt{3}}{2} \)
- \( \cos 30^\circ = \frac{\sqrt{3}}{2} \)
- \( \cos 60^\circ = \frac{1}{2} \)
- \( \sin 30^\circ = \frac{1}{2} \)

### Step 2: Substitute the values into the expression
Now, substitute these values into the expression:
\[ \sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ = \left(\frac{\sqrt{3}}{2}\right)\left(\frac{\sqrt{3}}{2}\right) + \left(\frac{1}{2}\right)\left(\frac{1}{2}\right) \]

### Step 3: Calculate each term
Calculate the first term:
\[ \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} = \frac{3}{4} \]
Calculate the second term:
\[ \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} \]

### Step 4: Add the results
Now, add the two results together:
\[ \frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1 \]

### Final Answer
Thus, the value of \( \sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ \) is \( 1 \).

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