Question 243254
{{{4sin(x/4)cos(x/4)cos(x/2)=sin(x)}}}
<pre><font size = 4 color = "indigo"><b>
Write the {{{4}}} in the left side as {{{2*2}}}

{{{2*2sin(x/4)cos(x/4)cos(x/2)=sin(x)}}}

Put parentheses around {{{2sin(x/4)cos(x/4)}}}

{{{2*(2sin(x/4)cos(x/4))cos(x/2)=sin(x)}}}

Use the identity {{{sin(2alpha)=2sin(alpha)cos(alpha)}}}
using {{{alpha=x/4}}}, {{{sin(2*(x/4))=2sin(x/4)cos(x/4)}}}
or {{{sin(x/2)=2sin(x/4)cos(x/4)}}}
to replace what we just put in parentheses:

{{{2*(sin(x/2))cos(x/2)=sin(x)}}}
 
{{{2sin(x/2)cos(x/2)=sin(x)}}}

Now use that same identity again, {{{sin(2alpha)=2sin(alpha)cos(alpha)}}},
this time using {{{alpha=x/2}}}, {{{sin(2*(x/2))=2sin(x/2)cos(x/2)}}}
or {{{sin(x)=2sin(x)cos(x)}}} to replace the left side:

{{{sin(x)=sin(x)}}}

Edwin</pre>