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

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

Note that cos(2a) = 2cos^2 (a) - 1 is a well known trigonometric identity.
a in this case will be 2x.

Answer 2

Cos^-21/2=