Sin3x+sqrt(3)cos3x=1

[latex]sin3x+ \sqrt{3}cos3x=1 [/latex] [latex]2(\frac{1}{2}\sqrt{3}*cos3x+\frac{1}{2} sin3x)=1[/latex] [latex]2(sin(\frac{\pi}{3}cos3x+cos(\frac{\pi}{3}sin3x ) )=1[/latex] [latex]2cos(\frac{\pi}{6}-3x)= 1[/latex] [latex]cos(\frac{\pi}{6}-3x)=\frac{1}{2} [/latex] π/6 -3x=π/3 +2πn; n∈Z                      π/6 -3x=5π/3 +2πn; n∈Z -3x=π/6 +2πn; n∈Z                             -3x=3π/2 +2πn; n∈Z x=-π/18 -2πn/3 ; n∈Z                         x=-π/2 -2πn/2 ; n∈Z