Cos 2x=2 cos x-1 решите уравнение и найдите дискриминант

Question

Cos 2x=2 cos x-1 решите уравнение и найдите дискриминант

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Answer 1

Cos2x = 2cosx - 1
2cos(^2)x - 1 = 2cosx - 1
2cos(^2)x - 2cosx = 0
cosx = t  t∈[-1; 1] 
2t^2 - 2t = 0
D = 4 - 0 = 4
t1 = 2 + 2 / 2 * 2 = 4/4 = 1
t2 = 2 - 2 / 2 * 2 = 0/4 = 0
cosx = 1 => x = +-π + 2πn, n∈Z
cosx = 0 => x = +-π/2 + 2πn, n∈Z