Question 17673
f{x}=3cos^2{4x}+sin^2{4x}-cos{4x)-1=0
2cos^2{4x}+[cos^2{4x}+sin^2{4x}]-cos{4x)-1=0
2cos^2{4x}+[1]-cos{4x)-1=0
2cos^2{4x}-cos{4x)=0
cos(4x)[cos(4x)-1]=0
cos(4x)=0 ......or..cos(4x)-1=0
CASE ONE
4x=pie/2.....(if you know general solutions then 4x=2npie+pie/2Or 2npie-pie/2)
or.x=pie/8..{if you know general solutions then x=npie/2+pie/8Or npie/2-pie/8}
CASE TWO
cos(4x)=1
4x=0.......(if you know general solutions then 4x=2npie) 

x=0.....{if you know general solutions then x=npie/2)