If angles M and N measure ` 60 ^(@) and 30^(@) ` respectively , (sin M) ` xx` (cot N) = ?
A. 1/2
B. `sqrt 3//2`
C. 3/2
D. 0

Options

A. D
B. B
C. A
D. C

Answer

To solve the problem, we need to calculate \( \sin M \times \cot N \) where \( M = 60^\circ \) and \( N = 30^\circ \).

### Step-by-Step Solution:

1. **Identify the values of sin and cot**:
- We know that \( \sin 60^\circ = \frac{\sqrt{3}}{2} \).
- We also need to find \( \cot 30^\circ \).

2. **Calculate \( \cot 30^\circ \)**:
- Recall that \( \cot \theta = \frac{1}{\tan \theta} \).
- We know that \( \tan 30^\circ = \frac{1}{\sqrt{3}} \).
- Therefore, \( \cot 30^\circ = \frac{1}{\tan 30^\circ} = \sqrt{3} \).

3. **Substitute the values into the expression**:
- Now we substitute the values we found into the expression:
\[ \sin M \times \cot N = \sin 60^\circ \times \cot 30^\circ = \left( \frac{\sqrt{3}}{2} \right) \times \sqrt{3} \]

4. **Perform the multiplication**:
- Multiply the two fractions:
\[ \frac{\sqrt{3}}{2} \times \sqrt{3} = \frac{\sqrt{3} \times \sqrt{3}}{2} = \frac{3}{2} \]

5. **Final answer**:
- Therefore, the value of \( \sin M \times \cot N \) is \( \frac{3}{2} \).

### Conclusion:
The answer is \( \frac{3}{2} \), which corresponds to option C.

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