Statement- 1: If the sines of the angles of a triangle are in A.P., then the altitudes ef the triangle are also in A.P.
Statement-2: Twice the area of a triangle is equal to the product of the lengths of a side and the altitude on it.

Options

A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement- 2 is True.

Explanation

To solve the problem, we need to analyze both statements given in the question and determine their truth values.

### Step-by-Step Solution:

1. **Understanding Statement 1**:
- Statement 1 claims that if the sines of the angles of a triangle are in Arithmetic Progression (A.P.), then the altitudes of the triangle are also in A.P.
- We denote the angles of the triangle as \( A \), \( B \), and \( C \). Thus, we have \( \sin A \), \( \sin B \), and \( \sin C \) in A.P.
- This means \( 2\sin B = \sin A + \sin C \).

2. **Using the Sine Rule**:
- According to the Sine Rule, we have:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = k \]
- From this, we can express the sides in terms of \( k \):
\[ a = k \sin A, \quad b = k \sin B, \quad c = k \sin C \]

3. **Substituting into the A.P. Condition**:
- Substituting the values of \( a \), \( b \), and \( c \) into the A.P. condition gives:
\[ 2b = a + c \implies 2(k \sin B) = k \sin A + k \sin C \]
- Dividing through by \( k \) (assuming \( k \neq 0 \)):
\[ 2 \sin B = \sin A + \sin C \]

4. **Finding Altitudes**:
- The altitudes corresponding to sides \( a \), \( b \), and \( c \) can be expressed as:
\[ h_a = \frac{2\Delta}{a}, \quad h_b = \frac{2\Delta}{b}, \quad h_c = \frac{2\Delta}{c} \]
- Where \( \Delta \) is the area of the triangle.

5. **Expressing Altitudes in Terms of Sides**:
- Substituting the expressions for \( a \), \( b \), and \( c \):
\[ h_a = \frac{2\Delta}{k \sin A}, \quad h_b = \frac{2\Delta}{k \sin B}, \quad h_c = \frac{2\Delta}{k \sin C} \]

6. **Analyzing the Relationship**:
- We can express the relationship between the altitudes:
\[ \frac{1}{h_a}, \frac{1}{h_b}, \frac{1}{h_c} \]
- This leads us to conclude that \( h_a, h_b, h_c \) are in Harmonic Progression (H.P.) instead of A.P.

7. **Conclusion for Statement 1**:
- Since the altitudes are in H.P. and not A.P., **Statement 1 is false**.

8. **Understanding Statement 2**:
- Statement 2 states that twice the area of a triangle is equal to the product of the length of a side and the altitude on it.
- This is a well-known property of triangles and is indeed true.

9. **Final Evaluation**:
- Statement 1 is false, and Statement 2 is true. Therefore, the correct option is that Statement 1 is false, and Statement 2 is true.

### Final Answer:
- **Statement 1 is false, Statement 2 is true.** The correct option is **Option 4**.