What is the value of `(1/3 + "cosec"30^(@))` ?

Options

A. `(sqrt(6) + 1)//sqrt(3)`
B. `7//3`
C. `(4+sqrt(3))//2`
D. `(sqrt(3)+1)//2`

Answer

To solve the question, we need to find the value of \( \frac{1}{3} + \csc 30^\circ \).

### Step-by-Step Solution:

1. **Calculate \( \csc 30^\circ \)**:
- The cosecant function is the reciprocal of the sine function. Therefore, \( \csc 30^\circ = \frac{1}{\sin 30^\circ} \).
- We know that \( \sin 30^\circ = \frac{1}{2} \).
- Thus, \( \csc 30^\circ = \frac{1}{\frac{1}{2}} = 2 \).

2. **Add \( \frac{1}{3} \) and \( \csc 30^\circ \)**:
- Now we need to add \( \frac{1}{3} + 2 \).
- To add these two fractions, we can express \( 2 \) as a fraction with a denominator of 3:
\[ 2 = \frac{2 \times 3}{3} = \frac{6}{3} \]
- Now we can add:
\[ \frac{1}{3} + \frac{6}{3} = \frac{1 + 6}{3} = \frac{7}{3} \]

3. **Final Result**:
- Therefore, the value of \( \frac{1}{3} + \csc 30^\circ \) is \( \frac{7}{3} \).

### Conclusion:
The answer is \( \frac{7}{3} \).