Evalulate : `"cosec "32-sec58^(@)`.

Answer

To evaluate the expression \( \csc 32^\circ - \sec 58^\circ \), we can follow these steps:

### Step 1: Rewrite the secant function
We know that \( \sec \theta = \frac{1}{\cos \theta} \). Thus, we can rewrite \( \sec 58^\circ \) as:
\[ \sec 58^\circ = \frac{1}{\cos 58^\circ} \]

### Step 2: Use the complementary angle identity
We can use the identity that states \( \cos(90^\circ - \theta) = \sin \theta \). Therefore, we can express \( \cos 58^\circ \) as:
\[ \cos 58^\circ = \sin(90^\circ - 58^\circ) = \sin 32^\circ \]
Thus, we can rewrite \( \sec 58^\circ \) as:
\[ \sec 58^\circ = \frac{1}{\sin 32^\circ} \]

### Step 3: Rewrite the cosecant function
The cosecant function is defined as \( \csc \theta = \frac{1}{\sin \theta} \). Therefore, we can express \( \csc 32^\circ \) as:
\[ \csc 32^\circ = \frac{1}{\sin 32^\circ} \]

### Step 4: Substitute back into the expression
Now we can substitute our expressions for \( \csc 32^\circ \) and \( \sec 58^\circ \) back into the original expression:
\[ \csc 32^\circ - \sec 58^\circ = \frac{1}{\sin 32^\circ} - \frac{1}{\sin 32^\circ} \]

### Step 5: Simplify the expression
Now, we can simplify the expression:
\[ \frac{1}{\sin 32^\circ} - \frac{1}{\sin 32^\circ} = 0 \]

### Final Answer
Thus, the value of \( \csc 32^\circ - \sec 58^\circ \) is:
\[ \boxed{0} \]