Answer:
x = pi/8 + pi/2 *n x = 3pi/8 + pi /2 *n
Explanation:
cos ^2 ( 2x) - sin ^2 (2x) = 0
Substitute u = 2x
cos ^2 ( u) - sin ^2 (u) = 0
We know cos ^2(x)-sin ^2(x)=cos (2x)
cos ( 2u) =0
Replacing u with 2x
cos (2 *2x) =0
cos (4x) =0
cos u =0 when u = pi/2 + 2 pi n and 3pi/2 + 2 pi n where n is an integer
4x = pi/2+2 pi n 4x = 3pi/2+2pi n
x = pi/8 + pi/2 *n x = 3pi/8 + pi /2 *n