Question

sin2x=√3sinx как решить

Answer 1

$sin2x=sqrt3 sin x\ 2sin x cos x =sqrt3 sin x\ 2sin x cos x -sqrt3 sin x=0\ sin x(2cos x-sqrt3)=0\\ sin x=0\ x=kpi\\ 2cos x-sqrt3=0\ 2cos x=sqrt3\ cos x=dfrac{sqrt3}{2}\ x=-dfrac{pi}{6}+2kpi vee x=dfrac{pi}{6}+2kpi\\ boxed{x=k pi vee x=-dfrac{pi}{6}+2kpivee x=dfrac{pi}{6}+2kpi,, kinmathbb{Z}}$