Question

The period of \( 2 \sin 4x \cos 4x \) is:

• A. \( \frac{2\pi}{3} \)
• B. \( \frac{2\pi}{4} \)
• C. \( \frac{\pi}{2} \)
• D. \( \frac{\pi}{4} \)
• E. \( \pi \)

Hint:

The period of a sine or cosine function is \( \frac{2\pi}{|A|} \) where \( A \) is the coefficient of \( x \).

Answer 1

The Correct Option is D

The period of \( \sin A \cos A \) is given by \( \frac{2\pi}{|A|} \). 
Here, \( A = 4x \), so the period of \( 2 \sin 4x \cos 4x \) is: \[ \frac{2\pi}{4} = \frac{\pi}{4} \] Thus, the correct answer is \( \frac{\pi}{4} \).