SOLUTION: Find all the solutions to the equation. I need help trying to solve the following problem.
cos(2theta)+2cos^2(theta/2)=2
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-> SOLUTION: Find all the solutions to the equation. I need help trying to solve the following problem.
cos(2theta)+2cos^2(theta/2)=2
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Question 313656: Find all the solutions to the equation. I need help trying to solve the following problem.
cos(2theta)+2cos^2(theta/2)=2 Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! cos(2theta)+2cos^2(theta/2)=2
I'll use x, less typing
cos(2x)+2cos^2(x/2)=2
cos(2x) = 2cos^2(x) - 1
------------------------
2cos^2(x) - 1 + 2cos^2(x/2) = 2
2cos^2(x) + 2cos^2(x/2) = 3
y = x/2
2cos^2(2y) + 2cos^2(y) = 3
2(2cos^2(y) - 1)^2 + 2cos^2(y) = 3
8cos^4(y) - 8cos^2(y) + 2 + 2cos^2(y) = 3
8cos^4(y) - 6cos^2(y) - 1 = 0
A quadratic in cos^2(y)
cos^2(y) = 3/8 ± sqrt(17)/8 =~ 0.890388
cos(y) =~ 0.9436038
y =~ ± 19.334º
theta =~ ± 38.668º (principal value)
