If A,B,C,D be the angles of a cyclic quadrilateral, then
`sin A + sin B - sin C - sin D ="……….."`

Answer

To solve the problem, we need to find the value of the expression \( \sin A + \sin B - \sin C - \sin D \) given that \( A, B, C, D \) are the angles of a cyclic quadrilateral.

### Step-by-Step Solution:

1. **Understanding the Cyclic Quadrilateral**:
In a cyclic quadrilateral, the sum of the opposite angles is \( 180^\circ \). Therefore, we have:
\[ A + C = 180^\circ \quad \text{and} \quad B + D = 180^\circ \]

2. **Expressing \( \sin C \)**:
From the relationship \( A + C = 180^\circ \), we can express \( C \) as:
\[ C = 180^\circ - A \]
Using the sine identity \( \sin(180^\circ - \theta) = \sin \theta \), we find:
\[ \sin C = \sin(180^\circ - A) = \sin A \]

3. **Expressing \( \sin D \)**:
Similarly, from the relationship \( B + D = 180^\circ \), we can express \( D \) as:
\[ D = 180^\circ - B \]
Again, using the sine identity:
\[ \sin D = \sin(180^\circ - B) = \sin B \]

4. **Substituting Values into the Expression**:
Now we substitute \( \sin C \) and \( \sin D \) back into the original expression:
\[ \sin A + \sin B - \sin C - \sin D = \sin A + \sin B - \sin A - \sin B \]

5. **Simplifying the Expression**:
When we simplify the expression, we get:
\[ \sin A + \sin B - \sin A - \sin B = 0 \]

### Final Answer:
Thus, the value of \( \sin A + \sin B - \sin C - \sin D \) is:
\[ \boxed{0} \]