1) -√2Cos x Sin x = Cos x
-√2 Cos x Sin x -Cos x = 0
Cos x(-√2 Sin x - 1 ) = 0
Cos x = 0 или -√2Sin x - 1 = 0
x = π/2 + πk, k ∈Z -√2Sin x = 1
Sin x = -1/√2
x = (-1)^n arcSin (-1/√2) + nπ, n ∈Z
x = (-1)^n·(-π/4) + nπ, n ∈Z
x = (-1)^(n +1) ·π/4 + nπ, n ∈Z
2)2Cos x + 1 = 0 или √-Sin x -1 = 0
2Cos x = -1 √-Sin x = 1|² -Sin x = 1
Cos x = -1/2 -Sin x >0
x = +-arcCos(-1/2) + 2πk , k ∈Z Sin x = -1 (нет решения)
x = +- 2π/3 + 2πk , k ∈Z
3) Cos 2x = Cos x
2Cos² x - 1 - Cos x = 0
Решаем как квадратное
а) Cosx = 1 б) Cos x = -1/2
x = 2πk, k ∈Z x = +- arcCos(-1/2) + 2πn, n∈Z
x = +-2π/3 + 2πn, n ∈Z
4)√Cos 2x = 0 или tg2x - 1 = 0
2x = π/2 + πk , k ∈Z tg 2x = 1
x = π/4 + πk/2, k ∈Z 2x = π/4 + πn, n ∈Z
x = π/8 + πn/2, n ∈Z
5)Ctg x - Sin 2x = 0
Cosx/Sin x - 2Sin x Cos x= 0 |·Sin x ≠0
Cos x - 2Sin²x Cos x = 0
Cos x(1 - 2Sin²x) = 0
Cos x = 0 или 1 - 2Sin²x = 0
x = π/2 + πk , k ∈Z Sin²x = 1/2
Sin x = +-√1/2
a)Sin x = 1/√2
x = (-1)^n·π/4 + nπ, n ∈Z
б) Sin x = -1/√2
x = (-1)^(n +1)·π/4 + mπ, m∈Z