Question

sqrt3*sinx/4-cosx/4=0

Answer 1

2(√3/2*sinx/4-1/2*cosx/4)=0
2sin(x/4-π/6)=0
x/4-π/6=πn
x/4=π/6+πn
x=2π/3+4πn,n∈z

Answer 2

$sqrt{3} *sin frac{x}{4} -cos frac{x}{4} =0 |:cos frac{x}{4} neq 0$
$frac{ sqrt{3}*sin frac{x}{4} }{cos frac{x}{4} } - frac{cos frac{x}{4} }{cos frac{x}{4} } =0$
√3*tg(x/4)-1=0
√3*tg(x/4)=1
$tg frac{x}{4} = frac{1}{ sqrt{3} }$
$frac{x}{4} =arctg frac{1}{ sqrt{3} } + pi n,$ n∈Z
$frac{x}{4} = frac{ pi }{6} + pi n, n$∈Z  |*4
$x= frac{2 pi }{3} +4 pi n,$n∈Z