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

Question

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

Answer 1

2cos²x -0.5 sin 4x = 1
-(1 - 2cos²x) - 0.5 (2 sin 2x ·cos 2x) = 0
-cos 2x - sin 2x · cos 2x = 0
cos 2x (1 + sin 2x) = 0
1) cos 2x = 0
2x = 0.5π + πn    
x = 0.25π + 0.5πn    n∈Z
2) 1 + sin 2x = 0
sin 2x = -1
2x = -0.5π + 2πn
x = -0.25π + πn    n∈Z