what is the value of `(1 // sqrt(3) + cot 60^@)`?

Options

A. `3 sqrt(3) //2`
B. `7 //2 sqrt(3)`
C. `(4 + sqrt(3)) // 2 sqrt(3)`
D. `2 // sqrt(3)`

Answer

To solve the question, we need to find the value of \( \left( \frac{1}{\sqrt{3}} + \cot 60^\circ \right) \).

### Step-by-Step Solution:

1. **Identify the value of \( \cot 60^\circ \)**:
- From trigonometric identities, we know that \( \cot 60^\circ = \frac{1}{\tan 60^\circ} \).
- The value of \( \tan 60^\circ \) is \( \sqrt{3} \).
- Therefore, \( \cot 60^\circ = \frac{1}{\sqrt{3}} \).

2. **Substitute \( \cot 60^\circ \) into the expression**:
- Now, we substitute \( \cot 60^\circ \) back into the original expression:
\[ \frac{1}{\sqrt{3}} + \cot 60^\circ = \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{3}} \]

3. **Combine the fractions**:
- Since both fractions have the same denominator, we can add them directly:
\[ \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{3}} = \frac{1 + 1}{\sqrt{3}} = \frac{2}{\sqrt{3}} \]

4. **Final answer**:
- Thus, the value of \( \left( \frac{1}{\sqrt{3}} + \cot 60^\circ \right) \) is:
\[ \frac{2}{\sqrt{3}} \]

### Conclusion:
The final answer is \( \frac{2}{\sqrt{3}} \).