Question 1079106
.
<pre>
-sin(2x) = {{{sqrt(3)*sin(x)}}}  --->

-2sin(x)*cos(x) = {{{sqrt(3)*sin(x)}}}  --->

-2sin(x)*cos(x) - sqrt(3)*sin(x)}}} = 0  --->

{{{-2sin(x)*(cos(x)+sqrt(3)/2)}}} = 0  --->


The last equation deploys in two independent equations


1.  sin(x) = 0  with the solutions  x = 0  and  x = {{{pi}}}.


2.  {{{cos(x) + sqrt(3)/2}}} = 0,  which is the same as  cos(x) = {{{-sqrt(3)/2}}},  with the solutions  x = {{{2pi/3}}}  and x = {{{4pi/3}}}.


<U>Answer</U>.  The set of solutions  is  {0, {{{2pi/3}}}, {{{pi}}}, {{{4pi/3}}} }.
</pre>


{{{graph( 1000, 330, -1.5, 6.5, -2.5, 2.5,
          -sin(2x), sqrt(3)*sin(x)
)}}}


Plot y = -sin(2x)  (red)  and y =  {{{sqrt(3)*sin(x)}}}