Question 1151813
<pre>
We use two identities

     {{{sin(2theta)=2sin(theta)cos(theta)}}}
and
     {{{cos(theta)=2cos^2(theta)-1}}}

to prove:

{{{sin(4x)=8sin(x)cos^3(x)-4sin(x)cos(x)}}}

Begin with the left side:

{{{sin(4x)}}}

{{{sin(2(2x)^"")}}}

{{{2sin(2x)cos(2x)}}}

{{{2(2sin(x)cos(x)^"")(2cos^2(x)^""-1)}}}

{{{4sin(x)cos(x)(2cos^2(x)^""-1)}}}

{{{8sin(x)cos^3(x)-4sin(x)cos(x)}}}

Edwin</pre>