Question

sin3x+sqrt(3)cos3x=1

Answer 1

$sin3x+ sqrt{3}cos3x=1$
$2(frac{1}{2}sqrt{3}*cos3x+frac{1}{2} sin3x)=1$
$2(sin(frac{pi}{3}cos3x+cos(frac{pi}{3}sin3x ) )=1$
$2cos(frac{pi}{6}-3x)= 1$
$cos(frac{pi}{6}-3x)=frac{1}{2}$

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