Помогите решить уравнение. Срочно!! 2sin(π/4-x/3)+√2=0

Question

Помогите решить уравнение. Срочно!! 2sin(π/4-x/3)+√2=0

Answer 1

2sin(π/4-x/3)+√2=0

2sin(π/4-x/3)=-√2 | :2

сos(x/3+π/4)=-√2/2

x/3+π/4=πn-π+arccos(-√2/2)

x/3+π/4=πn+3π/4

x/3+π/4=πn-π/4

x/3=πn+π/2

x/3=πn-π/2 | : 1/3

Ответ:

x1=3πn+3π/2

x2=3π

Answer 2

2sin(π/4-x/3)+√2=0

2sin(π/4-x/3) = - √2

sin(π/4-x/3) = -√2/2

π/4-x/3 = (-1)^n arcSin(-√2/2) +nπ, n ∈Z

π/4-x/3 = (-1)^n *π/4 +nπ, n ∈Z

-х/3 = (-1)^n π/4 + nπ -π/4 , n ∈Z

x = (-1)^(n+1) 3π/4 - 3πn -3π/4, n∈Z