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

Question

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

Quizplus · Accepted Answer

The given expression is in the form of the half-angle formula for cosine, which is $\cos(\frac{\theta}{2}) = \sqrt{\frac{1 + \cos(\theta)}{2}}$. Here, $\theta = 8x$, so the expression simplifies to $\cos(4x)$, or more accurately, $\cos|4x|$ to account for the absolute value in the options.

Use the Half-Angle Formula to Simplify the Given Expression 1+cos⁡8x2\sqrt { \frac { 1 + \cos 8 x } { 2 } }21+cos8x​​

Use the Half-Angle Formula to Simplify the Given Expression $\sqrt { \frac { 1 + \cos 8 x } { 2 } }$