SOLUTION: Find all solutions in the interval [0, 2pi) Cos^2 (x/2) = cos^2 x

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Question 741244: Find all solutions in the interval [0, 2pi)
Cos^2 (x/2) = cos^2 x
Answer by lwsshak3(11628) About Me  (Show Source):
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Find all solutions in the interval [0, 2pi)
Cos^2 (x/2) = cos^2 x
cos%5E2%28x%2F2%29=cos%5E2%28x%29
cos%28x%2F2%29=sqrt%28%281%2Bcos%28x%29%29%2F2%29%29
%281%2Bcos%28x%29%29%2F2=cos%5E2%28x%29
2cos^2(x)-cos(x)-1=0
(2cos(x)+1)(cos(x)-1)=0
cos(x)=-1/2
x=2π/3, 4π/3 (in Q2 and Q3 where cos<0)
cos(x)-1=0
cos(x)=1
x=0