Choose the correct answer in each of the following questions:
`(sec 30^(@))/("cosec"60^(@))=?`

Options

A. `(2)/(sqrt(3))`
B. `(sqrt(3))/(2)`
C. `sqrt(3)`
D. 1

Answer

To solve the expression \((\sec 30^\circ)/(\csc 60^\circ)\), we will follow these steps:

### Step 1: Identify the values of \(\sec 30^\circ\) and \(\csc 60^\circ\)

1. **Calculate \(\sec 30^\circ\)**:
- Recall that \(\sec \theta = \frac{1}{\cos \theta}\).
- Therefore, \(\sec 30^\circ = \frac{1}{\cos 30^\circ}\).
- The value of \(\cos 30^\circ\) is \(\frac{\sqrt{3}}{2}\).
- Thus, \(\sec 30^\circ = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}}\).

2. **Calculate \(\csc 60^\circ\)**:
- Recall that \(\csc \theta = \frac{1}{\sin \theta}\).
- Therefore, \(\csc 60^\circ = \frac{1}{\sin 60^\circ}\).
- The value of \(\sin 60^\circ\) is \(\frac{\sqrt{3}}{2}\).
- Thus, \(\csc 60^\circ = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}}\).

### Step 2: Substitute the values into the expression

Now we substitute the values we found into the expression:

\[ \frac{\sec 30^\circ}{\csc 60^\circ} = \frac{\frac{2}{\sqrt{3}}}{\frac{2}{\sqrt{3}}} \]

### Step 3: Simplify the expression

When we divide \(\frac{2}{\sqrt{3}}\) by \(\frac{2}{\sqrt{3}}\):

\[ \frac{\frac{2}{\sqrt{3}}}{\frac{2}{\sqrt{3}}} = 1 \]

### Final Answer

Thus, the value of \((\sec 30^\circ)/(\csc 60^\circ)\) is \(1\).