Statement 1: The function f (x) = sin x is symmetric about the line x = 0.
Statement 2: Every even function is symmetric about y-axis.

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 analyze the statements given in the question, we will evaluate each statement step by step.

### Step 1: Evaluate Statement 1
**Statement 1:** The function \( f(x) = \sin x \) is symmetric about the line \( x = 0 \).

**Analysis:**
- A function is symmetric about the line \( x = 0 \) (the y-axis) if \( f(-x) = f(x) \) for all \( x \).
- Let's calculate \( f(-x) \):
\[ f(-x) = \sin(-x) = -\sin x \]
- Since \( f(-x) \neq f(x) \), this means \( f(x) = \sin x \) is not symmetric about the y-axis.

**Conclusion for Statement 1:**
- Statement 1 is **false**.

### Step 2: Evaluate Statement 2
**Statement 2:** Every even function is symmetric about the y-axis.

**Analysis:**
- An even function is defined by the property \( f(-x) = f(x) \) for all \( x \).
- This definition implies that the graph of the function is a mirror image across the y-axis.

**Conclusion for Statement 2:**
- Statement 2 is **true**.

### Final Conclusion
- Statement 1 is false, and Statement 2 is true.

### Summary of Results
- **Statement 1:** False
- **Statement 2:** True