Question

\( \sqrt{2} \left( \sin \frac{\pi}{4} + \cos \frac{\pi}{4} \right) =\)

• A. \( \sqrt{2} \)
• B. 2
• C. 1
• D. \( \frac{1}{2} \)

Hint:

When adding \( \sin \) and \( \cos \) of the same angle, use the identity \( \sin^2 \theta + \cos^2 \theta = 1 \) to simplify.

Answer 1

The Correct Option is A

Step 1: Use the fact that \( \sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2} \). Step 2: Substituting these values: \[ \sqrt{2} \left( \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} \right) = \sqrt{2} \cdot \sqrt{2} = 2 \] Thus, the correct answer is \( \boxed{2} \).