Решите уравнение 2sin^2x+cosx=1

sin^2(x) + cos^2(x) = 1 - основное тригонометрическое тождество

2*(1 - cos^2(x)) = cosx + 1

2 - 2cos^2(x) = cosx + 1

2cos^2(x) + cosx - 1 = 0

Замена: cosx = t, t∈[-1;1]

2t^2 + t - 1 = 0, D=9

t1 = (-1 - 3)/4 = -4/4 = -1

t2 = (-1 + 3)/4 = 2/4 = 1/2

1) cosx = -1, x = π + 2πk

2) cosx = 1/2, x = +-π/3 + 2πk