2 cos^2 t + sin t + 1=0

Решение

2 cos^2 t + sin t + 1=0

2 * (1 - sin ²t) + sint + 1 = 0

2 - 2sin²t + sint + 1 = 0

2sin²t - sint - 3 = 0

sint = y, IyI ≤ 1

2y² - y - 3 = 0

D = 1 + 4*2*3 = 25

y₁ = (1 - 5) / 4

y₁ = - 1

y₂ = (1 + 5) / 4

y ₂ = 3/2 не удовлетворяет условию IyI ≤ 1

sint = - 1

t = - π/2 + 2πk, k ∈ Z