how does cos^2(2x)= (1/2)(1+cos4x)

Question

i dont understand how the squared equation gets transferred into the half angle identity

 

Answer 1

We know that double angle identity Cos2x = 2Cos^2x-1

Add 1 to each side.

1+Cos2x = 2Cos^2x

Cos^2x = (1+Cos2x)/2

If we assume x = 2x

Cos^2(2x) = (1+Cos2(2x))/2

Cos^2x = (1+Cos4x)/2

Cos^2x = 1/2(1+Cos4x)