Find the value of `cos^2 17^@ -sin^2 73^@`

Answer

To solve the problem of finding the value of \( \cos^2 17^\circ - \sin^2 73^\circ \), we can use some trigonometric identities.

### Step 1: Use the complementary angle identity
We know that:
\[ \sin(90^\circ - x) = \cos(x) \]
Thus, we can rewrite \( \sin 73^\circ \) as:
\[ \sin 73^\circ = \cos(90^\circ - 73^\circ) = \cos 17^\circ \]

### Step 2: Substitute the identity into the expression
Now we substitute \( \sin 73^\circ \) in our original expression:
\[ \cos^2 17^\circ - \sin^2 73^\circ = \cos^2 17^\circ - \cos^2 17^\circ \]

### Step 3: Simplify the expression
Now, simplifying the expression gives:
\[ \cos^2 17^\circ - \cos^2 17^\circ = 0 \]

### Conclusion
Thus, the value of \( \cos^2 17^\circ - \sin^2 73^\circ \) is:
\[ \boxed{0} \]