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

Using the half-angle formula for cosine, we have:

cos^2(2x) = (1 + cos(4x))/2

Rearranging, we get:

cos(4x) = 2cos^2(2x) - 1

Using the half-angle formula again, we have:

cos(x) = sqrt((1 + cos(2x))/2)

Substituting cos(2x) = 2cos^2(x) - 1, we get:

cos(x) = sqrt((1 + 2cos^2(x) - 1)/2)

cos(x) = |cos(x)|

Therefore, the answer is C, |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 $\sqrt { \frac { 1 + \cos 8 x } { 2 } }$