3*(1-sin^2 x) - sin x - 1 =0 3 - 3 sin^2 x - sin x - 1 = 0 2 - 3 sin^2 x - sin x = 0 3 sin^2 x+sin x - 2 = 0 Пусть sin x = t; t∈(-1;1) 3t²+t-2 = 0 D=1+24 = 25 = 5 ² t1 = (-1-5)/6 = -1 t2 = (-1+5)/6 = 4/6 = 2/3 Вернёмся к замене. sin x = -1 sin x = 2/3 x = -П+2Пn, n∈Z x = (-1)^k * arcsin(2/3) + Пk, k ∈ Z
3 - 3 sin^2 x - sin x - 1 = 0
2 - 3 sin^2 x - sin x = 0
3 sin^2 x+sin x - 2 = 0
Пусть sin x = t; t∈(-1;1)
3t²+t-2 = 0
D=1+24 = 25 = 5 ²
t1 = (-1-5)/6 = -1
t2 = (-1+5)/6 = 4/6 = 2/3
Вернёмся к замене.
sin x = -1
sin x = 2/3
x = -П+2Пn, n∈Z
x = (-1)^k * arcsin(2/3) + Пk, k ∈ Z