`sin^(2)88^(@)+cos^(2)88^(@)=?`

Options

A. `(1)/(2)`
B. `sqrt(3)`
C. 1
D. `(1)/(3)`

Answer

To solve the question \( \sin^2(88^\circ) + \cos^2(88^\circ) \), we can use the Pythagorean identity in trigonometry, which states:

\[ \sin^2(\theta) + \cos^2(\theta) = 1 \]

### Step-by-step Solution:

1. **Identify the angle**: In this case, the angle \( \theta \) is \( 88^\circ \).

2. **Apply the identity**: According to the Pythagorean identity, we can substitute \( \theta \) with \( 88^\circ \):
\[ \sin^2(88^\circ) + \cos^2(88^\circ) = 1 \]

3. **Conclude the result**: Therefore, the value of \( \sin^2(88^\circ) + \cos^2(88^\circ) \) is:
\[ 1 \]

### Final Answer:
\[ \sin^2(88^\circ) + \cos^2(88^\circ) = 1 \]