Statement I: If `A,B,C,D` are angles of a cyclic quadrilateral then `sum sin A=0.`
Statement II: If `A, B, C, D` are angles of cyclic quadrilateral then `sum cos A=0.`

Options

A. (a) Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I
B. (b) Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I
C. (c) Statement I is correct but Statement II is incorrect
D. (d) Statement II is correct but Statement I is incorrect

Answer

To solve the problem, we need to analyze the statements regarding the angles of a cyclic quadrilateral.

### Step-by-Step Solution:

1. **Understanding the Properties of Cyclic Quadrilaterals:**
A cyclic quadrilateral is a four-sided figure where all vertices lie on a single circle. The key property of cyclic quadrilaterals is that the sum of the opposite angles is supplementary. This means:
\[ A + C = 180^\circ \quad \text{and} \quad B + D = 180^\circ \]

2. **Analyzing Statement I:**
The first statement claims that the sum of the sines of the angles is zero:
\[ \sin A + \sin B + \sin C + \sin D = 0 \]
Since we know that \(C = 180^\circ - A\) and \(D = 180^\circ - B\), we can express \(\sin C\) and \(\sin D\) as:
\[ \sin C = \sin(180^\circ - A) = \sin A \quad \text{and} \quad \sin D = \sin(180^\circ - B) = \sin B \]
Therefore, the sum becomes:
\[ \sin A + \sin B + \sin A + \sin B = 2\sin A + 2\sin B \]
Since both \(\sin A\) and \(\sin B\) are positive for angles in the range \(0^\circ < A, B < 180^\circ\), the sum \(2\sin A + 2\sin B\) is always greater than zero. Thus, **Statement I is incorrect**.

3. **Analyzing Statement II:**
The second statement claims that the sum of the cosines of the angles is zero:
\[ \cos A + \cos B + \cos C + \cos D = 0 \]
Using the same substitutions for \(C\) and \(D\):
\[ \cos C = \cos(180^\circ - A) = -\cos A \quad \text{and} \quad \cos D = \cos(180^\circ - B) = -\cos B \]
Therefore, the sum becomes:
\[ \cos A + \cos B - \cos A - \cos B = 0 \]
This shows that **Statement II is correct**.

4. **Conclusion:**
Based on the analysis:
- Statement I is incorrect.
- Statement II is correct.

Thus, the correct answer is that **Statement 2 is correct but Statement 1 is incorrect**.

### Final Answer:
The correct option is **d**: Statement 2 is correct but Statement 1 is incorrect.