Question

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

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

Hint:

Remember trigonometric values of standard angles for quick calculations.

Answer 1

The Correct Option is B

Since \( \sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}} \):
\[ \sin \frac{\pi}{4} + \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \sqrt{2} \] \[ \sqrt{2} \times \sqrt{2} = 2 \]