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

Question

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

Quizplus · Accepted Answer

The half-angle formula for cosine is $\cos^2 \theta = \frac{1 + \cos 2\theta}{2}$. Here, $\theta = 4x$, so $\cos^2 4x = \frac{1 + \cos 8x}{2}$. Therefore, $\sqrt{\frac{1 + \cos 8x}{2}} = |\cos 4x|$.

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

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