Question

If \( A = 45^\circ \), then the value of \( \sin A + \cos A + \cos 2A \) is?

• A. \( \sqrt{2} \)
• B. 1
• C. \( 2 \)
• D. 0

Hint:

For \( A = 45^\circ \), use the known values of trigonometric functions to simplify expressions.

Answer 1

The Correct Option is A

Step 1: Use the values of trigonometric functions for \( A = 45^\circ \).
We know that:
\( \sin 45^\circ = \cos 45^\circ = \frac{\sqrt{2}}{2} \)
\( \cos 2A = \cos 90^\circ = 0 \)
Step 2: Substitute the values into the expression. \[ \sin 45^\circ + \cos 45^\circ + \cos 90^\circ = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} + 0 = \sqrt{2} \]