Evaluate `sin(30^(@)+theta)-cos(60^(@)-theta)`.

Answer

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

### Step 1: Write down the expression
We start with the expression:
\[ \sin(30^\circ + \theta) - \cos(60^\circ - \theta) \]

### Step 2: Use the sine and cosine identities
We know from trigonometric identities that:
\[ \sin(30^\circ) = \frac{1}{2} \quad \text{and} \quad \cos(60^\circ) = \frac{1}{2} \]

### Step 3: Substitute the values
Now, we can rewrite the expression using the sine and cosine addition formulas:
\[ \sin(30^\circ + \theta) = \sin(30^\circ)\cos(\theta) + \cos(30^\circ)\sin(\theta) \]
\[ \cos(60^\circ - \theta) = \cos(60^\circ)\cos(\theta) + \sin(60^\circ)\sin(\theta) \]

### Step 4: Substitute the known values
Substituting the known values:
\[ \sin(30^\circ + \theta) = \frac{1}{2}\cos(\theta) + \frac{\sqrt{3}}{2}\sin(\theta) \]
\[ \cos(60^\circ - \theta) = \frac{1}{2}\cos(\theta) + \frac{\sqrt{3}}{2}\sin(\theta) \]

### Step 5: Substitute back into the expression
Now substituting these back into our original expression:
\[ \left(\frac{1}{2}\cos(\theta) + \frac{\sqrt{3}}{2}\sin(\theta)\right) - \left(\frac{1}{2}\cos(\theta) + \frac{\sqrt{3}}{2}\sin(\theta)\right) \]

### Step 6: Simplify the expression
When we simplify this, we see that both terms are identical and will cancel each other out:
\[ \frac{1}{2}\cos(\theta) + \frac{\sqrt{3}}{2}\sin(\theta) - \frac{1}{2}\cos(\theta) - \frac{\sqrt{3}}{2}\sin(\theta) = 0 \]

### Final Answer
Thus, the value of the expression \( \sin(30^\circ + \theta) - \cos(60^\circ - \theta) \) is:
\[ \boxed{0} \]