Question

$sqrt{3} sin frac{x}{4} -cos frac{x}{4}=0$
$3sin ^{2} x-2sinx*cosx-5cos ^{2} x=0$

Answer 1

$sqrt{3}sin frac{x}{4} -cos frac{x}{4} =0$

$2( frac{ sqrt{3} }{2} sin frac{x}{4} - frac{1}{2} cos frac{x}{4})=0$

$frac{ sqrt{3} }{2} sin frac{x}{4} - frac{1}{2} cos frac{x}{4}=0$

$frac{ sqrt{3} }{2} =cos frac{ pi }{6}, frac{1}{2} =sin frac{ pi }{6}$

$cos frac{ pi }{6}sin frac{x}{4} -sin frac{ pi }{6} cos frac{x}{4} =0$

$sin( frac{x}{4} - frac{ pi }{6} )=0$

$frac{x}{4} - frac{ pi }{6} = pi k,$ k∈Z

$frac{x}{4} = frac{ pi }{6} +pi k,$ k∈Z

$x= frac{2 pi }{3}+ frac{ pi }{4} k,$ k∈Z