Question

$2^2 \sin(\frac{x}{2^2}) \cos(\frac{x}{2}) \cos(\frac{x}{2^2}) =$

• A. $\sin 2x$
• B. $\sin x$
• C. $\cos 2x$
• D. $\cos^2 x$
• E. $\sin \frac{x}{2}$

Hint:

When you see a chain of cosines with halving angles, look for the sine double angle identity.

Answer 1

The Correct Option is B

Step 1: Concept
Use the double angle formula $2\sin \theta \cos \theta = \sin 2\theta$.

Step 2: Analysis
Group the terms: $[2 \sin(\frac{x}{4}) \cos(\frac{x}{4})] \cdot 2 \cos(\frac{x}{2})$. The first part becomes $\sin(\frac{x}{2})$.

Step 3: Calculation
Now we have $2 \sin(\frac{x}{2}) \cos(\frac{x}{2})$. This equals $\sin(2 \cdot \frac{x}{2}) = \sin x$. Final Answer: (B)