SOLUTION: Find all solutions to the equation below on the interval [0, 2π). Enter them from smallest to largest; enter DNE in any empty blank. cos (2x) + cos (x) = 2 x = x = TH

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions to the equation below on the interval [0, 2π). Enter them from smallest to largest; enter DNE in any empty blank. cos (2x) + cos (x) = 2 x = x = TH      Log On


   

Question 927037: Find all solutions to the equation below on the interval [0, 2π). Enter them from smallest to largest; enter DNE in any empty blank.
cos (2x) + cos (x) = 2
x =
x =
THANKS
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions to the equation below on the interval [0, 2π). Enter them from smallest to largest; enter DNE in any empty blank.
cos%282x%29%2Bcosx=2
cos%5E2%28x%29-sin%5E2%28x%29%2Bcosx=2
cos%5E2%28x%29-%281-cos%5E2%28x%29%29%2Bcosx=2
cos%5E2%28x%29-1%2Bcos%5E2%28x%29%2Bcosx=2
2cos^2(x)+cosx-3=0
(2cosx+3)(cosx-1)=0
2cosx+3=0
cosx=-3/2 (reject,-1 ≤ cosx ≤ 1
or
(cosx-1)=0
cosx=1
x=0