SOLUTION: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter

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Question 865061: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
cos (2θ) = cos^2 θ − (1/2)

Found 2 solutions by lwsshak3, stanbon:
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
For interval (0,2π)
cos (2θ) = cos^2 θ − (1/2)
cos^2 θ -sin^2 θ =cos^2 θ -1/2
sin^2 θ =1/2
sin θ =�1/√2=�√2/2
θ =π/4, 3π/4, 5π/4, 7π/4

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
cos (2θ) = cos^2 θ − (1/2)
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2cos^2(t)-1 = cos^2(t) - (1/2)
cos^2(t) = 1/2
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cos(t) = +-sqrt(2)/2)
t = pi/4 or (3/4)pi or (5/4)pi or (7/4)pi
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Cheers,
Stan H.