Assertion : In `x = A cos omega t`, `x` is the displacement measured from extreme position.
Reason : In the above equation `x = A` at time `t = 0`.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To analyze the assertion and reason provided in the question, we will break down the statements step by step.

### Step 1: Understanding the Assertion
The assertion states that in the equation \( x = A \cos(\omega t) \), \( x \) is the displacement measured from the extreme position.

**Explanation**:
- In simple harmonic motion (SHM), the displacement \( x \) represents how far the object is from its equilibrium position at any given time \( t \).
- The extreme positions in SHM are the maximum displacements from the equilibrium position, which are \( +A \) and \( -A \).
- Therefore, the assertion is correct because \( x \) is indeed measured from the extreme positions.

### Step 2: Understanding the Reason
The reason states that in the equation \( x = A \cos(\omega t) \), \( x = A \) at time \( t = 0 \).

**Explanation**:
- At \( t = 0 \), substituting into the equation gives:
\[ x = A \cos(0) = A \cdot 1 = A \]
- This means that at \( t = 0 \), the displacement \( x \) is equal to the amplitude \( A \), which corresponds to one of the extreme positions.
- Thus, the reason is also correct.

### Step 3: Connecting the Assertion and Reason
Now we need to determine if the reason correctly explains the assertion.

- The assertion claims that \( x \) is the displacement from the extreme position, and the reason shows that at \( t = 0 \), the displacement is indeed at one of the extreme positions (specifically at \( x = A \)).
- Since both statements are true and the reason provides a valid explanation for the assertion, we conclude that the reason is a correct explanation of the assertion.

### Final Conclusion
Both the assertion and reason are true, and the reason correctly explains the assertion. Therefore, the answer to the question is:

**Both the assertion and reason are true, and the reason is the correct explanation of the assertion.**