Choose the correct answer in each of the following questions:
`sec^(2)60^(@)-1=?`

Options

A. 2
B. 3
C. 4
D. 0

Explanation

To solve the question \( \sec^2(60^\circ) - 1 \), we will follow these steps:

### Step 1: Find \( \sec(60^\circ) \)
The secant function is defined as the reciprocal of the cosine function:
\[ \sec(60^\circ) = \frac{1}{\cos(60^\circ)} \]

### Step 2: Calculate \( \cos(60^\circ) \)
From trigonometric values, we know:
\[ \cos(60^\circ) = \frac{1}{2} \]

### Step 3: Substitute \( \cos(60^\circ) \) into the secant formula
Now substituting the value of \( \cos(60^\circ) \) into the secant function:
\[ \sec(60^\circ) = \frac{1}{\frac{1}{2}} = 2 \]

### Step 4: Calculate \( \sec^2(60^\circ) \)
Now we need to square the value of \( \sec(60^\circ) \):
\[ \sec^2(60^\circ) = (2)^2 = 4 \]

### Step 5: Compute \( \sec^2(60^\circ) - 1 \)
Now we can substitute this value back into the original expression:
\[ \sec^2(60^\circ) - 1 = 4 - 1 = 3 \]

### Final Answer
Thus, the value of \( \sec^2(60^\circ) - 1 \) is \( 3 \).