2 +cos^2 x-3 cos x =0

Question

2 +cos^2 x-3 cos x =0

Answer 1

2 + cos²x - 3cosx = 0
cos²x - 3cosx + 2 = 0
Пусть t = cosx, t ∈ [-1; 1].
t² - 3t + 2 = 0
t1 + t2 = 3
t1•t2 = 2

t1 = 2 - не уд. условию
t2 = 1

Обратная замена:
cosx = 1
x = 2πn, n ∈ Z.