The problem is to evaluate the expression $\sin^2(2561^\circ) + \cos^2(2561^\circ)$.

1. Problem Description

The problem is to evaluate the expression $\sin^2(2561^\circ) + \cos^2(2561^\circ)$.

2. Solution Steps

We can use the Pythagorean trigonometric identity, which states that for any angle $\theta$:

$\sin^2(\theta) + \cos^2(\theta) = 1$

In our case, $\theta = 2561^\circ$. Therefore, we have:

$\sin^2(2561^\circ) + \cos^2(2561^\circ) = 1$

3. Final Answer

1