2cos^2(2t)=1-cos2t Find all solutions

2cos^2(2t)=1-cos2t Find all solutions

There are infinitely many solutions so we need boundaries, assuming 0 ≤ t ≤ 360.

2cos²(2t) = 1 - cos(2t)
2cos²(2t) + cos(2t) - 1 = 0
[2cos(2t) - 1][cos(2t) + 1] = 0
2cos(2t) - 1 = 0 OR cos(2t) = -1
cos(2t) = ½ OR cos(2t) = -1
(2t)ᵣ = 60° OR (2t)ᵣ = 0°
2t = 60°, 300°, 420°, 660° OR 2t = 180°, 540°
t = 30°, 150°, 210°, 330° OR t = 90°, 270°
t = 30°, 90°, 150°, 210°, 270°, 330°

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2cos^2(2t)-1+cos2t=0
2cos 2t( cos 2t+1)-1( cos 2t+1)=0
either cos 2t=-1 or cos2t=1/2

2cos^2 t-1=-1 2cos^2 t-1=1/2
2cos^2 t=0 cos^2=3/4
cos t=1 or cos t=-1 cost=.8666 or cos t=-.866666
t=0 or 180 t=30,-30 or 330 t=150, 210 or -150

U can write general solution by adding 2n pi in each solution