Evaluate:
`(sec 75^(@))/(cosec 15^(@))`

Answer

To evaluate the expression \(\frac{\sec 75^\circ}{\csc 15^\circ}\), we can follow these steps:

### Step 1: Rewrite \(\csc 15^\circ\)
We know that \(\csc \theta = \frac{1}{\sin \theta}\). Therefore, we can rewrite \(\csc 15^\circ\) as:
\[ \csc 15^\circ = \frac{1}{\sin 15^\circ} \]

### Step 2: Substitute into the expression
Now, substituting this into our original expression gives us:
\[ \frac{\sec 75^\circ}{\csc 15^\circ} = \sec 75^\circ \cdot \sin 15^\circ \]

### Step 3: Rewrite \(\sec 75^\circ\)
We know that \(\sec \theta = \frac{1}{\cos \theta}\). Thus, we can rewrite \(\sec 75^\circ\) as:
\[ \sec 75^\circ = \frac{1}{\cos 75^\circ} \]

### Step 4: Substitute \(\sec 75^\circ\) into the expression
Substituting this into our expression gives us:
\[ \frac{1}{\cos 75^\circ} \cdot \sin 15^\circ \]

### Step 5: Use the complementary angle identity
We can use the identity \(\cos(90^\circ - \theta) = \sin \theta\). Therefore, we have:
\[ \cos 75^\circ = \sin(90^\circ - 75^\circ) = \sin 15^\circ \]

### Step 6: Substitute \(\cos 75^\circ\)
Now substituting \(\cos 75^\circ\) back into our expression gives us:
\[ \frac{1}{\sin 15^\circ} \cdot \sin 15^\circ \]

### Step 7: Simplify the expression
Now we can simplify:
\[ \frac{\sin 15^\circ}{\sin 15^\circ} = 1 \]

### Final Answer
Thus, the value of \(\frac{\sec 75^\circ}{\csc 15^\circ}\) is:
\[ \boxed{1} \]