document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167730>Question 167730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Verify this identity :\r<BR>\n" );
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document.write( "sin4x = (cosx)(4sinx-8sin^3x)\r<BR>\n" );
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document.write( "Here is what I've shamefully accomplished so far :\r<BR>\n" );
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document.write( "=(cosx)4sinx(1-2sin^2x)<BR>\n" );
document.write( "=(cosx)4sinx(cos2x)<BR>\n" );
document.write( "=(cos3x)(4sinx)<BR>\n" );
document.write( "=???????\r<BR>\n" );
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document.write( "Now I'm stuck!  Any insight would be appreciated greatly! Thank you in advance for your time!!\r<BR>\n" );
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document.write( "Desperately seeking solution, Rebecca </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123642 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=cos(x)(4sin(x)-8sin^3(x)) \"> ... Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=cos(x)4sin(x)(1-2sin(x)) \"> ... Factor out <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 4sin(x)\"> (good so far)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=4sin(x)cos(x)(1-2sin(x)) \"> Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=2*2sin(x)cos(x)(1-2sin(x)) \"> Factor 4 into 2*2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=2sin(2x)(1-2sin(x)) \"> Use the identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2sin(x)cos(x)=sin(2x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=2sin(2x)cos(2x) \"> Use the identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 1-2sin(x)=cos(2x)\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2x ALIGN=MIDDLE  ALT=\"z=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=2sin(z)cos(z) \"> Substitute \"z\" in for 2x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=sin(2z) \"> Use the identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2sin(z)cos(z)=sin(2z)\"> (similar to the previous used identity just with a different variable)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=sin(2*2x) \"> Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2x ALIGN=MIDDLE  ALT=\"z=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=sin(4x) \"> Multiply\r<BR>\n" );
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document.write( "Since both sides of the equation are equal, this means that we've verified the identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin(4x)=cos(x)(4sin(x)-8sin^3(x)) \"> </SPAN>\n" );
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