Question 864419
Sin 2x=(square-root 3) sin x
{{{sin(2x)=sqrt(3)sin(x)}}}
Double Angle Identity,
{{{sin(2x)=2*sin(x)cos(x)=sqrt(3)sin(x)}}}
{{{2*sin(x)cos(x)-sqrt(3)sin(x)=0}}}
{{{sin(x)(2*cos(x)-sqrt(3))=0}}}
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Either {{{sin(x)=0}}} OR {{{2*cos(x)-sqrt(3)=0}}}.
The first alternative means, {{{highlight(x=0)}}} or {{{highlight(x=2*pi)}}}.
The second alternative means,
{{{2*cos(x)=sqrt(3)}}}
{{{cos(x)=sqrt(3)/2}}}, meaning {{{highlight(x=pi/3)}}}.