Question

sin^2(3x)=3cos^2(3x)

Answer 1

$frac{1 - cos(6x) }{2} = frac{3(1 + cos(6x)) }{2}$
$3 + 3 cos(6x) - 1 + cos(6x) = 0$
$4 cos(6x) = - 2$
$cos(6x) = - frac{1}{2}$
$6x = + - frac{2}{3} pi + 2pi times k$
$x = + - frac{pi}{9} + frac{pi times k}{3}$