Question 335877
Solve this equation for {{{"[0,"}}}{{{2pi}}}{{{")"}}}:
{{{Sin(4x) - Sin(2x)=0}}}
<pre><b>
Write {{{4}}} in the first term as {{{2*2}}}  

{{{Sin(2*2x) - Sin(2x)=0}}}

Use the identity {{{Sin(2theta)=2*Sin(theta)*Cos(theta)}}} with {{{theta=2x}}}
to replace the first term:

{{{2*Sin(2x)*Cos(2x) - Sin(2x)=0}}}

Factor out {{{Sin(2x)}}} on the left:

{{{Sin(2x)(2Cos(2x)-1)=0}}}

Set each factor on the left = 0

{{{matrix(3,5,

Sin(2x)=0,  "", "", "", 2*Cos(2x)-1=0,
"",         "", "", "", 2*Cos(2x)=1,
"",         "", "", "", Cos(2x)=1/2)}}}

Notice that the coefficient of x is 2.
Since we want all values x in the interval
{{{"[0,"}}}{{{2pi}}}{{{")"}}}, we must find all values for 
2x in the interval {{{"[0,"}}}{{{4pi}}}{{{")"}}}

{{{matrix(3,13,

"", "", Sin(2x)=0, "", "", "", "", "","","",Cos(2x)=1/2,"","",

2x=0,2x=pi,2x=2pi,2x=3pi,"", "","","","",2x=pi/3,2x=5pi/3,2x=7pi/3,2x=11pi/3,
x=0,x=pi/2,x=pi,x=(3pi)/2,"","","","","",x=pi/6,x=5pi/6,x=7pi/6,x=11pi/6
)}}}

So there are 8 solutions. 
  
Edwin</pre>