Question 1078659
.
<pre>
{{{sin(2x)}}} = {{-sqrt(3)*sin(x)}}}  --->  (Use the formula sin(2x) = 2*sin(x)*cos(x). You will get )

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

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

xin(x)*(2*cos(x)+sqrt(3)) = 0 .


Then the last equation deploys in two independent equations.


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


2.  2*cos(x) + sqrt(3) = 0  --->  cos(x) = {{{-sqrt(3)/2}}} with the solutions

    x = {{{2pi/3}}} and  x = {{{4pi/3}}}.


<U>Answer</U>.  The solutions to the given equations are x= 0, x= {{{2pi/3}}}, x = {{{pi}}} and x= {{{4pi/3}}}.
</pre>


{{{graph( 1200, 400, -0.5, 6.5, -2.5, 2.5,
          sin(2x), -sqrt(3)*sin(x)
)}}}


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



You have many solved similar problems in this site. See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solving-simple-problems-on-trigonometric-equations.lesson>Solving simple problems on trigonometric equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solving-typical-problems-on-trigonometric-equations.lesson>Solving typical problems on trigonometric equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solving-more-complicated-problems-on-trigonometric-equations.lesson>Solving more complicated problems on trigonometric equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solved-problems-on-trigonometric-equations.lesson>Solving advanced problems on trigonometric equations</A>


These solved problems are samples for you to learn from.



Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Trigonometry: Solved problems</U>".