What is the value of (tan`30^@-sqrt3//2`) ?

Options

A. `-1//2sqrt3`
B. `(2sqrt3-sqrt6)//2sqrt2`
C. `(2-sqrt3)//2`
D. `1//6`

Answer

To find the value of \( \tan 30^\circ - \frac{\sqrt{3}}{2} \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the value of \( \tan 30^\circ \)**:
\[ \tan 30^\circ = \frac{1}{\sqrt{3}} \]

2. **Substitute \( \tan 30^\circ \) into the expression**:
\[ \tan 30^\circ - \frac{\sqrt{3}}{2} = \frac{1}{\sqrt{3}} - \frac{\sqrt{3}}{2} \]

3. **Find a common denominator**:
The common denominator for \( \sqrt{3} \) and \( 2 \) is \( 2\sqrt{3} \).

4. **Rewrite each term with the common denominator**:
\[ \frac{1}{\sqrt{3}} = \frac{2}{2\sqrt{3}} \quad \text{and} \quad \frac{\sqrt{3}}{2} = \frac{\sqrt{3} \cdot \sqrt{3}}{2\sqrt{3}} = \frac{3}{2\sqrt{3}} \]

5. **Combine the fractions**:
\[ \frac{2}{2\sqrt{3}} - \frac{3}{2\sqrt{3}} = \frac{2 - 3}{2\sqrt{3}} = \frac{-1}{2\sqrt{3}} \]

6. **Final result**:
\[ \tan 30^\circ - \frac{\sqrt{3}}{2} = \frac{-1}{2\sqrt{3}} \]

### Final Answer:
\[ \boxed{\frac{-1}{2\sqrt{3}}} \]