document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=920239>Question 920239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I simplify this?\r<BR>\n" );
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document.write( "Working with radians here.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558250 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=558250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To start things off, I'm going to expand out each piece being added\r<BR>\n" );
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document.write( "Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29+=+sin%28pi%2F2%29cos%28x%29-cos%28pi%2F2%29sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29+=+sin%28pi%2F2%29cos%28x%29-cos%28pi%2F2%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29+=+1%2Acos%28x%29-0%2Asin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29+=+1%2Acos%28x%29-0%2Asin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29+=+cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29+=+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi-x%29 ALIGN=MIDDLE  ALT=\"sin%28pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi-x%29=sin%28pi%29cos%28x%29-cos%28pi%29sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi-x%29=sin%28pi%29cos%28x%29-cos%28pi%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi-x%29=0%2Acos%28x%29-%28-1%29sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi-x%29=0%2Acos%28x%29-%28-1%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi-x%29=sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi-x%29=sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%283pi%2F2-x%29 ALIGN=MIDDLE  ALT=\"sin%283pi%2F2-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%283pi%2F2-x%29+=+sin%283pi%2F2%29cos%28x%29-cos%283pi%2F2%29sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%283pi%2F2-x%29+=+sin%283pi%2F2%29cos%28x%29-cos%283pi%2F2%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%283pi%2F2-x%29+=+-1%2Acos%28x%29-0%2Asin%28x%29 ALIGN=MIDDLE  ALT=\"sin%283pi%2F2-x%29+=+-1%2Acos%28x%29-0%2Asin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%283pi%2F2-x%29+=+-cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%283pi%2F2-x%29+=+-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282pi-x%29 ALIGN=MIDDLE  ALT=\"sin%282pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282pi-x%29=sin%282pi%29cos%28x%29-cos%282pi%29sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%282pi-x%29=sin%282pi%29cos%28x%29-cos%282pi%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282pi-x%29=0%2Acos%28x%29-1%2Asin%28x%29 ALIGN=MIDDLE  ALT=\"sin%282pi-x%29=0%2Acos%28x%29-1%2Asin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282pi-x%29=-sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%282pi-x%29=-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "So we know the following:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29+=+cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29+=+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi-x%29=sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi-x%29=sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%283pi%2F2-x%29+=+-cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%283pi%2F2-x%29+=+-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282pi-x%29=-sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%282pi-x%29=-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "Which will be used below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29+=+cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29+=+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29+%2Bsin%28x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29+%2Bsin%28x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi-x%29 ALIGN=MIDDLE  ALT=\"sin%28pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi-x%29+=+sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28pi-x%29+=+sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29+%2Bsin%28x%29%2B%28-cos%28x%29%29%2Bsin%282pi-x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29+%2Bsin%28x%29%2B%28-cos%28x%29%29%2Bsin%282pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%283pi%2F2-x%29 ALIGN=MIDDLE  ALT=\"sin%283pi%2F2-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-cos%28x%29 ALIGN=MIDDLE  ALT=\"-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%283pi%2F2-x%29+=+-cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%283pi%2F2-x%29+=+-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29+%2Bsin%28x%29%2B%28-cos%28x%29%29%2B%28-sin%28x%29%29 ALIGN=MIDDLE  ALT=\"cos%28x%29+%2Bsin%28x%29%2B%28-cos%28x%29%29%2B%28-sin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282pi-x%29 ALIGN=MIDDLE  ALT=\"sin%282pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sin%28x%29 ALIGN=MIDDLE  ALT=\"-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282pi-x%29+=+-sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%282pi-x%29+=+-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29+%2Bsin%28x%29-cos%28x%29-sin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29+%2Bsin%28x%29-cos%28x%29-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28x%29-cos%28x%29%29%2B%28sin%28x%29-sin%28x%29%29 ALIGN=MIDDLE  ALT=\"%28cos%28x%29-cos%28x%29%29%2B%28sin%28x%29-sin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29%2B%280%29 ALIGN=MIDDLE  ALT=\"%280%29%2B%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B0 ALIGN=MIDDLE  ALT=\"0%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So in the end, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2-x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29=0 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2-x%29+%2Bsin%28pi-x%29%2Bsin%283pi%2F2-x%29%2Bsin%282pi-x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an identity (true for all real numbers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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