Question

√2*cos(2x/3+pi/4)=1
Помогите решить (желательно подробно)

Answer 1

cos(2x/3+π/4)=1/√2
cos(2x/3+π/4)=√2/2
2x/3+π/4= + - π/4 + 2πn, n∈Z

1) 2x/3 +π/4 = π/4 + 2πn, n∈Z
2x/3 = π/4 - π/4 + 2πn
2x/3 = 2πn
x= (3/2) * 2πn
x= 3πn,  n∈Z

2) 2x/3 +π/4 = -π/4 +2πn, n∈Z
2x/3 = -π/4 - π/4 + 2πn
2x/3 = -π/2 + 2πn
x= (3/2) *(-π/2) + (3/2)*(2πn)
x= -3π/4 + 3πn, n∈Z

Ответ: -3π/4 + 3πn, n∈Z;
             3πn, n∈Z.