Given o

We have to solve cos 4x = 1 for values of x that satisfy
0<=x<=2*pi

cos 4x = cos
2*2x

=> 1 - 2(sin
2x)^2

=> 1 - 2*(2*cos x * sin
x)^2

=> 1 - 8*(cos x)^2*(sin
x)^2

=> 1 - 8*(1 - (sin x)^2)(sin
x)^2

let (sin x)^2 =
y

=> 1 - 8*(1 - y)y =
1

=> (1 - y)y =
0

=> y = 0 and y =
1

sin x = 0

=> x = arc
sin 0

=> x = 0, pi ,
2*pi

(sin x)^2 = 1

=> x
= arc sin 1 and x = arc sin (-1)

=> x = pi/2 and x =
3*pi/2

The required solution of the equation
is x = {0 , pi/2, pi , 3*pi/2, 2*pi}