1) 1 - Sin²x - Sinx -5/9 = 0 | * 9
9 - 9Sin²x -9Sinx -5 = 0
9Sin²x + 9Sinx -4 = 0
Sinx = y
9y² + 9y - 4= 0
D = b² - 4ac = 81 - 4*9*(-4) = 81 + 144 = 225
y = -8+15/18= 1/6
у = -23/18
а)Sinx = 1/16
х = (-1)ⁿ arcSin(1/6) + nπ, n ∈Z
б) Sinx = -23/18
нет решений.
Ответ: х = (-1)ⁿ arcSin(1/6) + nπ, n ∈Z
2) Sin²x + Cos²x - Sin²x + 3SinxCosx -2*1 = 0
Cos²x +3SinxCosx -2(Sin²x + Cos²x) = 0
Cos²x + 3SinxCosx -2Sin²x -2Cos²x = 0
-Cos²x + 3SinxCosx -2Sin²x= 0 | : Cos²x ≠ 0
-1 + 3tgx -2tg²x = 0
2tg²x - 3tgx +1 = 0
tgx = y
2y² - 3y +1 = 0
D = 1
y = 1 и у = 1/2
а) tgx = 1
x = π/4 + πk , k ∈Z
б) tgx = 1/2
x = arctg(1/2) + πn , n ∈Z
3) Cos²x/2 - 2Sinx/2Cosx/2 +2Sin²x/2 -Sin²x/2 - Cos²x/2 = 0
Sin²x/2 -2Sinx/2Cosx/2 = 0
Sinx/2(Sinx/2 - 2Cosx/2) = 0
Sinx/2 = 0 или Sinx/2 -2Cosx/2 = 0| : Cosx/2
x/2 = πn , n ∈Z tg x/2 -2 = 0
x = 2πn, n ∈∈Z tgx/2 = 2
x/2 = arctg2 + πk, k ∈Z
x = 2arctg2 + 2πk , k ∈Z