Question

Решите!!!
2синус^2 х +3синусх= 2

Answer 1

2sin²(x) + 3sin(x) = 2
1 - cos2x + 3sinx = 2
1 - cos²x + sin²x + 3sinx = 2
2sin²x + 3sinx - 2 = 0
a = sinx
2a² + 3a - 2 = 0
D = 9 - 4 * 2 * (-2) = 25
a1,2 = (-3 ± 5)/4
a1 = -2
a2 = 1/2
sinx = -2 (быть не может)
sinx = 1/2 
x = p/6