The problem asks to simplify the expression $\cos^2(\frac{\pi}{12}) - \sin^2(\frac{\pi}{12})$.

1. Problem Description

The problem asks to simplify the expression $\cos^2(\frac{\pi}{12}) - \sin^2(\frac{\pi}{12})$.

2. Solution Steps

We can use the trigonometric identity:

$\cos(2x) = \cos^2(x) - \sin^2(x)$

In this case, $x = \frac{\pi}{12}$. So, we have

$\cos^2(\frac{\pi}{12}) - \sin^2(\frac{\pi}{12}) = \cos(2 \cdot \frac{\pi}{12}) = \cos(\frac{\pi}{6})$

We know that $\cos(\frac{\pi}{6}) = \cos(30^\circ) = \frac{\sqrt{3}}{2}$.

3. Final Answer

$\frac{\sqrt{3}}{2}$