2 sin 3 x +2 cos 3 x=√2

Question

2 sin 3 x +2 cos 3 x=√2

Answer 1

2(sin3x+cos3x)=√2
√2sin(3x+π/4)=√2/2
sin(3x+π/4)=1/2
3x+π/4=(-1)^n*π/6+πn, n∈z
3x=(-1)^n*π/6-π/4+πn, n∈z
x=(-1)^n*π/18-π/12+π/3n, n∈z
Ответ. x=(-1)^n*π/18-π/12+π/3n, n∈z