Statement (A) : `tan50^(@)gt1`
Reason (R ) : For `0^(@)ltthetalt90^(@), tanthetagt1`

Options

A. a)Both A and R are correct and R is the correct explanation of A .
B. b)Both A and R are correct but R is not a correct explanation of A .
C. c)A is correct, R is incorrect .
D. d)A is incorrect, R is correct .

Answer

To solve the given question, we need to analyze the statement (A) and the reason (R) provided.

### Step-by-Step Solution:

**Step 1: Evaluate Statement (A)**
- The statement (A) claims that \( \tan(50^\circ) > 1 \).
- We know that \( \tan(45^\circ) = 1 \) and \( \tan(60^\circ) = \sqrt{3} \approx 1.732 \).
- Since \( 50^\circ \) is between \( 45^\circ \) and \( 60^\circ \), and the tangent function is increasing in this interval, we can conclude that \( \tan(50^\circ) \) must be greater than \( \tan(45^\circ) \).
- Therefore, \( \tan(50^\circ) > 1 \) is **true**.

**Step 2: Evaluate Reason (R)**
- The reason (R) states that for \( 0^\circ < \theta < 90^\circ \), \( \tan(\theta) > 1 \).
- This is not entirely true because \( \tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.577 < 1 \).
- Hence, while it is true that \( \tan(\theta) \) is greater than 1 for angles greater than \( 45^\circ \) and less than \( 90^\circ \), it is not true for all angles in the interval \( (0^\circ, 90^\circ) \).
- Therefore, the reason (R) is **false**.

**Step 3: Conclusion**
- Statement (A) is true, and Reason (R) is false.
- Thus, the correct option is that the statement is correct but the reason is incorrect.

### Final Answer:
- **C**: Statement (A) is correct but Reason (R) is incorrect.