`cos^(2)73^(@)+cos^(2)47^(@)-sin^(2)43^(@)+sin^(2)107^(@)` is equal to

Options

A. `1//2`
B. `3//4`
C. 1
D. none of these

Explanation

To solve the expression \( \cos^2 73^\circ + \cos^2 47^\circ - \sin^2 43^\circ + \sin^2 107^\circ \), we can simplify it step by step.

### Step 1: Rewrite the cosine terms
Using the identity \( \cos(90^\circ - \theta) = \sin(\theta) \), we can rewrite \( \cos^2 73^\circ \) and \( \cos^2 47^\circ \):

\[ \cos^2 73^\circ = \sin^2(90^\circ - 73^\circ) = \sin^2 17^\circ \]
\[ \cos^2 47^\circ = \sin^2(90^\circ - 47^\circ) = \sin^2 43^\circ \]

### Step 2: Substitute into the expression
Now we substitute these identities back into the original expression:

\[ \sin^2 17^\circ + \sin^2 43^\circ - \sin^2 43^\circ + \sin^2 107^\circ \]

### Step 3: Simplify the expression
Notice that \( \sin^2 43^\circ \) and \( -\sin^2 43^\circ \) cancel each other out:

\[ \sin^2 17^\circ + \sin^2 107^\circ \]

### Step 4: Rewrite \( \sin^2 107^\circ \)
Using the identity \( \sin(90^\circ + \theta) = -\cos(\theta) \), we can rewrite \( \sin^2 107^\circ \):

\[ \sin^2 107^\circ = \sin^2(90^\circ + 17^\circ) = \cos^2 17^\circ \]

### Step 5: Substitute and simplify
Now we substitute this back into our expression:

\[ \sin^2 17^\circ + \cos^2 17^\circ \]

### Step 6: Apply the Pythagorean identity
Using the Pythagorean identity \( \sin^2 \theta + \cos^2 \theta = 1 \):

\[ \sin^2 17^\circ + \cos^2 17^\circ = 1 \]

### Final Answer
Thus, the value of the expression \( \cos^2 73^\circ + \cos^2 47^\circ - \sin^2 43^\circ + \sin^2 107^\circ \) is:

\[ \boxed{1} \]