SOLUTION: Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 8 cos3 x = 8 cos x

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 8 cos3 x = 8 cos x       Log On


   

Question 911429: Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
8 cos3 x = 8 cos x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
8%2Acos%283x%29+=+8%2Acos%28x%29
cos%283x%29=cos%28x%29
4cos%5E3%28x%29-3cos%28x%29=cos%28x%29
Let u=cos%28x%29
4u%5E3-3u=u
4u%5E3-4u=0
u%28u%5E2-1%29=0
u%28u%2B1%29%28u-1%29=0
Three solutions,
u=0
cos%28x%29=0
x=pi%2F2
.
.
u%2B1=0
u=-1
cos%28x%29=-1
x=pi
.
.
u-1=0
u=1
cos%28x%29=1
x=0
.
.
.
0,pi%2F2,pi