1) sin^2x+6sinx-6=0
Пусть sinx = t, причём t ∈ [ -1; 1]
t^2 + 6t - 6 = 0
D = 36 + 24 = 60
√D = 2√15
t 1 = ( - 6 + 2√15)/2 = - 3 + √15 ≈ 0,87
t2 = - 3 - √15 ==> ∉ [ -1; 1]
sinx = √15 - 3
x = (-1)^k arcsin(√15-3) + pik, k ∈Z
2) cos^2x + 8sinx = 3
1 - sin^2x + 8sinx - 3 = 0
sin^2x - 8sinx + 2 = 0
Пусть sinx = t, причём t ∈ [ -1; 1]
t^2 - 8t + 2 = 0
D = 64 - 8 = 56
t= 4 - √14
sinx = 4 - √14
x = (-1)^k arcsin(4-√14) + pik, k ∈Z