Решите уравнение 2sin^2 x-cos x-1=0

Question

Решите уравнение
2sin^2 x-cos x-1=0

Answer 1

2*(1 - cos^2(x)) - cosx - 1 = 0
2 - 2cos^2(x) - cos(x) - 1 = 0
-2cos^2(x) - cos(x) + 3 = 0
2cos^2(x) + cos(x) - 3 = 0
Замена: cos(x) = t, -1 ≤ t ≤ 1
2t^2 + t - 3 = 0
D = 1 + 4*3*2 = 1 + 24 = 25
t1 = (-1 - 5)/4 = -6/4 = -3/2 < -1 - посторонний корень
t2 = (-1 + 5)/4 = 4/4 = 1
cosx = 1, x = 2πk