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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:


Evaluate the expression (cos(π/4) + sin(π/6))^2 without using a calculator.

Step-by-step solution to evaluate (cos(π/4) + sin(π/6))^2 using trigonometric values. Understand how to combine and simplify trigonometric expressions. Ideal for students in Grades 9-11.

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