What is the value of `sin(30+x)-cos(60-x)` ?

Options

A. 1
B. 2
C. 0
D. `(1)/(2)`

Answer

To find the value of \( \sin(30 + x) - \cos(60 - x) \), we can simplify the expression step by step.

### Step 1: Use the known values of sine and cosine
We know that:
- \( \sin(30^\circ) = \frac{1}{2} \)
- \( \cos(60^\circ) = \frac{1}{2} \)

### Step 2: Rewrite the expression
We can rewrite the expression as:
\[ \sin(30 + x) - \cos(60 - x) = \sin(30 + x) - \sin(90 - (60 - x)) \]
Using the identity \( \cos(A) = \sin(90 - A) \), we have:
\[ \cos(60 - x) = \sin(90 - (60 - x)) = \sin(30 + x) \]

### Step 3: Substitute the known values
Now, substituting the values we have:
\[ \sin(30 + x) - \sin(30 + x) = 0 \]

### Conclusion
Thus, the value of \( \sin(30 + x) - \cos(60 - x) \) is:
\[ \boxed{0} \]