SOLUTION: algebraically find exact values for all of the roots of the function (i.e. solve f(x)=0 for all values of x (in radians)). Give exact answers only. f{x}=3cos^2{4x}+sin^2{4x}-cos{

Question 17673: algebraically find exact values for all of the roots of the function (i.e. solve f(x)=0 for all values of x (in radians)). Give exact answers only.
f{x}=3cos^2{4x}+sin^2{4x}-cos{4x)-1
final answer: X is element________
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
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)

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