Question

Simplify \( \sqrt{2} + \sqrt{2} + 2 \cos 4\theta = \)

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

Hint:

When simplifying trigonometric expressions, look for opportunities to apply basic trigonometric identities or algebraic manipulations to reduce the expression.

Answer 1

The Correct Option is A

Step 1: Understand the problem.
The given expression is \( \sqrt{2} + \sqrt{2} + 2 \cos 4\theta \). First, simplify the terms that involve constants. We have \( \sqrt{2} + \sqrt{2} = 2\sqrt{2} \).
Step 2: Use trigonometric identities.
Now, consider the trigonometric term \( 2 \cos 4\theta \). Since \( 4\theta \) can be simplified using angle identities, the equation simplifies to: \[ 2\sqrt{2} \cos \theta \]
Step 3: Conclusion.
Thus, the simplified result is \( 2 \cos \theta \).