Use the half-angle formula to simplify the given expression.
$$\sqrt { \frac { 1 + \cos 16 x } { 2 } }$$
A) $\cos 32 x$
B) $\cos 8 x$
C) $\cos 16 x$
D) $\cos 64 x$
E) $\cos 4 x$

Question

Quizplus · Accepted Answer

Using the half-angle formula, we have:
$$\cos^2(8x) = \frac{1 + \cos(16x)}{2}$$
Therefore,
$$\sqrt{\frac{1 + \cos(16x)}{2}} = \sqrt{\cos^2(8x)} = |\cos(8x)|$$
Since the expression is always non-negative, we can drop the absolute value and conclude that
$$\sqrt{\frac{1 + \cos(16x)}{2}} = \cos(8x)$$ 
Therefore, the correct answer is $\boxed{\textbf{(B)}}$.

Use the Half-Angle Formula to Simplify the Given Expression 1+cos⁡16x2\sqrt { \frac { 1 + \cos 16 x } { 2 } }21+cos16x​​

Use the Half-Angle Formula to Simplify the Given Expression $\sqrt { \frac { 1 + \cos 16 x } { 2 } }$