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

Answer

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

### Step 1: Identify the values of the trigonometric functions.
We need to know the values of the following trigonometric functions:
- \( \sin 60^\circ \)
- \( \cos 30^\circ \)
- \( \cos 60^\circ \)
- \( \sin 30^\circ \)

### Step 2: Write down the known values.
From trigonometric tables or the unit circle, we have:
- \( \sin 60^\circ = \frac{\sqrt{3}}{2} \)
- \( \cos 30^\circ = \frac{\sqrt{3}}{2} \)
- \( \cos 60^\circ = \frac{1}{2} \)
- \( \sin 30^\circ = \frac{1}{2} \)

### Step 3: Substitute the values into the expression.
Now we 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 4: Simplify the expression.
Now we simplify each term:
\[ = \frac{3}{4} + \frac{1}{4} \]

### Step 5: Combine the fractions.
Now we combine the fractions:
\[ = \frac{3 + 1}{4} = \frac{4}{4} = 1 \]

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

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