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 solve the given problem, we need to analyze both statements regarding the function \( f(x) = \sin x \) and the definition of even functions.

### Step 1: Analyze Statement 1
The first statement claims that the function \( f(x) = \sin x \) is symmetric about the line \( x = 0 \).

**Definition of Symmetry:**
A function is symmetric about the y-axis (or the line \( x = 0 \)) if for every \( x \), \( f(-x) = f(x) \).

**Check for \( \sin x \):**
Let's check if \( \sin(-x) = \sin x \):
\[ \sin(-x) = -\sin x \]
This shows that \( \sin x \) is not symmetric about the y-axis. Instead, \( \sin x \) is an odd function, which means it is symmetric about the origin (not the y-axis).

**Conclusion for Statement 1:**
Thus, Statement 1 is **False**.

### Step 2: Analyze Statement 2
The second statement asserts that every even function is symmetric about the y-axis.

**Definition of Even Functions:**
A function \( f(x) \) is called even if:
\[ f(-x) = f(x) \]
for all \( x \) in the domain of \( f \).

**Implication of Even Functions:**
If a function satisfies this property, it means that the graph of the function on the left side of the y-axis mirrors the graph on the right side. Therefore, it is indeed symmetric about the y-axis.

**Conclusion for Statement 2:**
Thus, Statement 2 is **True**.

### Final Conclusion
Based on the analysis:
- Statement 1 is False.
- Statement 2 is True.

The correct option is that Statement 1 is False and Statement 2 is True, which corresponds to **Option 4**.