`cos^(2)20^(@)+cos^(2)70^(@)` is equal to :

Options

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

Answer

To solve the expression \( \cos^2(20^\circ) + \cos^2(70^\circ) \), we can utilize the trigonometric identity that relates cosine and sine.

### Step-by-Step Solution:

1. **Write the expression**:
\[ \cos^2(20^\circ) + \cos^2(70^\circ) \]

2. **Use the identity for cosine**:
We know that \( \cos(90^\circ - \theta) = \sin(\theta) \). Therefore, we can rewrite \( \cos(70^\circ) \):
\[ \cos(70^\circ) = \sin(20^\circ) \]
Hence, \( \cos^2(70^\circ) = \sin^2(20^\circ) \).

3. **Substitute into the expression**:
Now, we can substitute \( \cos^2(70^\circ) \) in our original expression:
\[ \cos^2(20^\circ) + \sin^2(20^\circ) \]

4. **Apply the Pythagorean identity**:
According to the Pythagorean identity, \( \cos^2(\theta) + \sin^2(\theta) = 1 \):
\[ \cos^2(20^\circ) + \sin^2(20^\circ) = 1 \]

5. **Final result**:
Therefore, the value of \( \cos^2(20^\circ) + \cos^2(70^\circ) \) is:
\[ \boxed{1} \]