SOLUTION: use the half angle identities to find all solutions in the interval [0,2pi) sin^2x=cos^2(x/2)

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Question 738948: use the half angle identities to find all solutions in the interval [0,2pi) sin^2x=cos^2(x/2)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
use the half angle identities to find all solutions in the interval [0,2pi) sin^2x=cos^2(x/2)
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sin%5E2%28x%29=cos%5E2%28x%2F2%29
cos%28x%2F2%29=sqrt%28%281%2Bcos%28x%29%29%2F2%29
cos%5E2%28x%2F2%29=%281%2Bcos%28x%29%29%2F2
sin%5E2%28x%29=%281%2Bcos%28x%29%29%2F2
2sin%5E2%28x%29=%281%2Bcos%28x%29%29
2%281-cos%5E2%28x%29%29=%281%2Bcos%28x%29%29
%282-2cos%5E2%28x%29%29=%281%2Bcos%28x%29%29
%282cos%5E2%28x%29%29%2Bcos%28x%29-1=0%29
%282cos%28x%29-1%29%28cos%28x%29%2B1%29=0
..
2cos(x)-1=0
cos(x)=1/2
x=π/3, 5π/3
..
cos(x)+1=0
cos(x)=-1
x=π