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 =

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 =       Log On


   

Question 925773: 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 =
Thank you
Answer by lwsshak3(11628) About Me  (Show Source):
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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
***
2cos^2(x)-1+cosx=2
2cos^2(x)+cosx-3=0
(2cosx+3)(cosx-1)=0
2cosx+3=0
cosx=-3/2 (reject,1 ≤ cosx ≤ 1)
..
cosx-1=0
cosx=1
x=0