The value of the expression `(cos^(2)23^(@)-sin^(2)67^(@))` is

Options

A. `1`
B. `2`
C. `3`
D. `0`

Explanation

To solve the expression \( \cos^2(23^\circ) - \sin^2(67^\circ) \), we can follow these steps:

### Step 1: Rewrite the sine term using the co-function identity
We know that:
\[ \sin(67^\circ) = \cos(90^\circ - 67^\circ) = \cos(23^\circ) \]
Thus, we can rewrite \( \sin^2(67^\circ) \) as:
\[ \sin^2(67^\circ) = \cos^2(23^\circ) \]

### Step 2: Substitute the sine term in the expression
Now we can substitute \( \sin^2(67^\circ) \) in the original expression:
\[ \cos^2(23^\circ) - \sin^2(67^\circ) = \cos^2(23^\circ) - \cos^2(23^\circ) \]

### Step 3: Simplify the expression
Now, simplifying the expression gives us:
\[ \cos^2(23^\circ) - \cos^2(23^\circ) = 0 \]

### Conclusion
The value of the expression \( \cos^2(23^\circ) - \sin^2(67^\circ) \) is:
\[ 0 \]