What is the value of `(sin22(1^(@))/(2)+cos22(1^(@))/(2))`?

Options

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

Explanation

To solve the expression \( \left( \sin^2\left(22.5^\circ\right) + \cos^2\left(22.5^\circ\right) \right) \), we can follow these steps:

### Step 1: Use the Pythagorean Identity
Recall the Pythagorean identity:
\[ \sin^2 \theta + \cos^2 \theta = 1 \]
For our case, we have:
\[ \sin^2(22.5^\circ) + \cos^2(22.5^\circ) = 1 \]

### Step 2: Rewrite the Expression
The original expression can be rewritten as:
\[ \sin^2(22.5^\circ) + \cos^2(22.5^\circ) = 1 \]

### Step 3: Conclusion
Thus, the value of the expression \( \left( \sin^2(22.5^\circ) + \cos^2(22.5^\circ) \right) \) is:
\[ \boxed{1} \]