Question

4 sin^2x+sinx-3=0 помогите срочно

Answer 1

4sin²x + sinx - 3 = 0
Пусть t = sinx, t ∈ [-1; 1]
4t² + t - 3 = 0
D = 1 + 4•4•3 = 49 = 7²
t1 = (-1 + 7)/8 = 6/8 = 3/4
t2 ° (-1 - 7)/8 = -8/8 = -1
Обратная замена:
sinx = 3/4
x = (-1)ⁿarcsin(3/4) + πn, n ∈ Z.
sinx = -1
x = -π/2 + 2πn, n ∈ Z.
Ответ: x = (-1)ⁿarcsin(3/4) + πn, n ∈ Z; x = -π/2 + 2πn, n ∈ Z.