Question

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

Answer 1

Решение
2 cos^2 t+ sin t +1=0
2*(1 - sin²t) + 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
y₂ = 3/2  не удовлетворяет условию IyI ≤ 1
sint = - 1
t = - π/2 + 2πk, k ∈ Z