Statement -1 : `sin 3 le sin 1 le sin2`
Statement-2 : `sinx ` is positive in the first and second quadrants .

Options

A. Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True and 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

Answer

To solve the problem, we need to evaluate the two statements provided:

**Statement 1:** \( \sin(3) < \sin(1) < \sin(2) \)

**Statement 2:** \( \sin(x) \) is positive in the first and second quadrants.

### Step 1: Evaluate Statement 1

1. **Convert radians to degrees:**
- \( \sin(1) \) in degrees:
\[ 1 \text{ radian} = \frac{180}{\pi} \approx 57.29^\circ \]
- \( \sin(2) \) in degrees:
\[ 2 \text{ radians} = \frac{360}{\pi} \approx 114.59^\circ \]
- \( \sin(3) \) in degrees:
\[ 3 \text{ radians} = \frac{540}{\pi} \approx 171.88^\circ \]

2. **Evaluate the sine values:**
- \( \sin(1) \approx 0.8415 \)
- \( \sin(2) \approx 0.9093 \)
- \( \sin(3) \approx 0.1411 \)

3. **Compare the sine values:**
- We need to check if \( \sin(3) < \sin(1) < \sin(2) \):
- \( 0.1411 < 0.8415 < 0.9093 \) is true.

Thus, **Statement 1 is true.**

### Step 2: Evaluate Statement 2

1. **Understanding the sine function:**
- The sine function is positive in the first quadrant (0 to \( \frac{\pi}{2} \)) and in the second quadrant (\( \frac{\pi}{2} \) to \( \pi \)).
- Therefore, \( \sin(x) \) is indeed positive in these quadrants.

Thus, **Statement 2 is also true.**

### Step 3: Determine the relationship between the statements

1. **Check if Statement 2 explains Statement 1:**
- Statement 2 states that \( \sin(x) \) is positive in the first and second quadrants, but it does not provide an explanation for why \( \sin(3) < \sin(1) < \sin(2) \).
- Therefore, while both statements are true, Statement 2 does not explain Statement 1.

### Conclusion

- **Statement 1 is true.**
- **Statement 2 is true.**
- **Statement 2 is not a correct explanation for Statement 1.**

Thus, the correct option is **B**: Statement 1 is true, Statement 2 is true, and Statement 2 is not a correct explanation for Statement 1.

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