SOLUTION: Solution for cos4x=cos2x

Question 770143: Solution for cos4x=cos2x

Found 2 solutions by tommyt3rd, Alan3354:
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
cos4x=cos2x
tells us that

which gives us

or

where n is an integer
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solution for cos4x=cos2x
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cos(2A) = 2cos^2(A) - 1 double angle formula
---
cos4x=cos2x
2cos^2(2x) - 1 = cos(2x)
2cos^2(2x) - cos(2x) - 1 = 0
(2cos + 1)*(cos - 1) = 0
cos(2x) = 1
2x = 0 + 2n*pi, n = 0,1,2,3...
x = 0 + n*pi, n = 0,1,2,3...
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cos(2x) = -1/2
2x = 2pi/3, 4pi/3 + 2n*pi, n = 0,1,2,3...
x = pi/3, 2pi/3 + n*pi, n = 0,1,2,3...

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