If `sinC-sinD=x` , then the value of x is

Options

A. `2sin[((C+D))/(2)]cos[((C-D))/(2)]`
B. `2cos[((C+D))/(2)]cos[((C-D))/(2)]`
C. `2cos[((C+D))/(2)]sin[((C-D))/(2)]`
D. `2sin[((C+D))/(2)]sin[((C-D))/(2)]`

Answer

To find the value of \( x \) given that \( \sin C - \sin D = x \), we can use the sine subtraction formula.

### Step-by-Step Solution:

1. **Recall the Sine Difference Formula**:
The formula for the difference of two sine functions is:
\[ \sin C - \sin D = 2 \cos\left(\frac{C + D}{2}\right) \sin\left(\frac{C - D}{2}\right) \]

2. **Apply the Formula**:
Using the formula, we can express \( x \) as:
\[ x = \sin C - \sin D = 2 \cos\left(\frac{C + D}{2}\right) \sin\left(\frac{C - D}{2}\right) \]

3. **Conclusion**:
Thus, the value of \( x \) is:
\[ x = 2 \cos\left(\frac{C + D}{2}\right) \sin\left(\frac{C - D}{2}\right) \]

### Final Answer:
\[ x = 2 \cos\left(\frac{C + D}{2}\right) \sin\left(\frac{C - D}{2}\right) \]