6(1 - sin^2x) + sinx - 5 = 0
6 - 6sin^2x + sinx - 5 = 0
- 6sin^2x + sinx + 1 = 0 /:(-1)
6sin^2x - sinx - 1 = 0
Пусть sinx = t, |t| ≤ 1
6t^2 - t - 1 = 0
D = 1 + 24 = 25
t1 = ( 1 + 5)/12 = 6/12 = 1/2
t2 = ( 1 - 5)/12 = - 4/12 = - 1/3
Обратная замена
sinx = 1/2
x1 = pi/6 + 2pik, k ∈ Z
x2 = 5pi/6 + 2pik, k ∈ Z
sinx = - 1/3
x3 = - arcsin(1/3) + 2pik , k∈ Z
x4 = pi + arcsin(1/3) + 2pik, k ∈Z