Use the half-angle formula to simplify the given expression.

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. ​
​  ​
A)​​cos |2x| 
B)​​cos |8x| 
C)​​cos |16x| 
D)​​cos |32x| 
E)​cos |4x|

Quizplus · Accepted Answer

The half-angle formula states that cos(2θ) = 1-2sin²θ or cos²θ- sin²θ. 
If we let θ = 2x, then we can apply the half-angle formula to get:
cos(4x) = cos²(2x) - sin²(2x) 
= (1 + cos(4x))/2 - (1 - cos(4x))/2 
= cos(4x)/2 + 1/2
Therefore, the simplified expression is cos |4x|.

Use the Half-Angle Formula to Simplify the Given Expression