What is the value of `(cot 60^@ + 1//sqrt3)`

Options

A. `4//sqrt3`
B. `(2sqrt2 + sqrt3)//2`
C. `2//sqrt3`
D. `(2sqrt2 + 1)//sqrt2`

Answer

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

### Step-by-step Solution:

1. **Find the value of \( \cot 60^\circ \)**:
- The cotangent function is defined as the reciprocal of the tangent function.
- Therefore, \( \cot 60^\circ = \frac{1}{\tan 60^\circ} \).
- We know that \( \tan 60^\circ = \sqrt{3} \).
- Thus, \( \cot 60^\circ = \frac{1}{\sqrt{3}} \).

2. **Add \( \frac{1}{\sqrt{3}} \) to \( \cot 60^\circ \)**:
- Now we substitute the value of \( \cot 60^\circ \) into the expression:
\[ \cot 60^\circ + \frac{1}{\sqrt{3}} = \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{3}} \]

3. **Combine the fractions**:
- Since both terms are the same, we can combine them:
\[ \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{3}} = \frac{2}{\sqrt{3}} \]

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