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

The given expression can be simplified using the half-angle formula for cosine, which is $\cos \frac{\theta}{2} = \sqrt{\frac{1 + \cos \theta}{2}}$. Here, $\theta = 16x$, so the expression simplifies to $\cos 8x$, matching option 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 $\sqrt { \frac { 1 + \cos 16 x } { 2 } }$