Let's evaluate the expression:

$\left( \cos\left(\frac{\pi}{4}\right) + \sin\left(\frac{\pi}{6}\right) \right)^2$

Step 1: Compute the values of the trigonometric functions.

• $\cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$
• $\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$

Step 2: Add the results.

$\frac{1}{\sqrt{2}} + \frac{1}{2}$ To add these fractions, let's express both terms with a common denominator. The common denominator between $\sqrt{2}$ and 2 is $2\sqrt{2}$. So, rewrite both fractions: $\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}, \quad \frac{1}{2} = \frac{\sqrt{2}}{\sqrt{2}} \times \frac{1}{2} = \frac{\sqrt{2}}{2}$

Thus: $\frac{\sqrt{2}}{2} + \frac{1}{2}$

Step 3: Combine terms: