Evaluate : `"cosec "31^(@)-sec 59^(@)`.

Answer

To evaluate the expression \( \csc 31^\circ - \sec 59^\circ \), we can follow these steps:

### Step 1: Rewrite the secant function
We know that:
\[ \sec \theta = \frac{1}{\cos \theta} \]
Thus, we can rewrite \( \sec 59^\circ \) as:
\[ \sec 59^\circ = \frac{1}{\cos 59^\circ} \]

### Step 2: Use the complementary angle identity
We can use the identity that states:
\[ \cos(90^\circ - \theta) = \sin \theta \]
This means:
\[ \cos 59^\circ = \sin(90^\circ - 59^\circ) = \sin 31^\circ \]
So, we can rewrite \( \sec 59^\circ \):
\[ \sec 59^\circ = \frac{1}{\sin 31^\circ} \]

### Step 3: Rewrite the cosecant function
We also know that:
\[ \csc \theta = \frac{1}{\sin \theta} \]
Thus, we can rewrite \( \csc 31^\circ \) as:
\[ \csc 31^\circ = \frac{1}{\sin 31^\circ} \]

### Step 4: Substitute back into the expression
Now, substituting these identities back into the original expression:
\[ \csc 31^\circ - \sec 59^\circ = \frac{1}{\sin 31^\circ} - \frac{1}{\sin 31^\circ} \]

### Step 5: Simplify the expression
Now, we can see that:
\[ \csc 31^\circ - \sec 59^\circ = \frac{1}{\sin 31^\circ} - \frac{1}{\sin 31^\circ} = 0 \]

### Final Answer
Thus, the value of \( \csc 31^\circ - \sec 59^\circ \) is:
\[ \boxed{0} \]