document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010663>Question 1010663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Will you please help me with this equation:  Given: sin (x+y)=sin x cos y + cos x sin y  and cos (x+y) = cos x cos y - sin x sin y.  Simplify ; sin ( x + pi ) × tan (x +pi/2) × sec (pi/2 - x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626264 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=626264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break the problem into smaller pieces\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%29+=+sin%28x%29%2Acos%28pi%29%2Bcos%28x%29%2Asin%28pi%29 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%29+=+sin%28x%29%2Acos%28pi%29%2Bcos%28x%29%2Asin%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the given identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%29+=+sin%28x%29%2A%28-1%29%2Bcos%28x%29%2A%280%29 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%29+=+sin%28x%29%2A%28-1%29%2Bcos%28x%29%2A%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the unit circle\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%29+=+-sin%28x%29%2B0 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%29+=+-sin%28x%29%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%29+=+-sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%29+=+-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. We'll call this Equation A\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%2F2%29+=+sin%28x%29%2Acos%28pi%2F2%29%2Bcos%28x%29%2Asin%28pi%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%2F2%29+=+sin%28x%29%2Acos%28pi%2F2%29%2Bcos%28x%29%2Asin%28pi%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the given identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%2F2%29+=+sin%28x%29%2A%280%29%2Bcos%28x%29%2A%281%29 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%2F2%29+=+sin%28x%29%2A%280%29%2Bcos%28x%29%2A%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the unit circle\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%2F2%29+=+0%2Bcos%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%2F2%29+=+0%2Bcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%2F2%29+=+cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%2F2%29+=+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. We'll call this Equation B\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2Bpi%2F2%29+=+cos%28x%29%2Acos%28pi%2F2%29-sin%28x%29sin%28pi%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28x%2Bpi%2F2%29+=+cos%28x%29%2Acos%28pi%2F2%29-sin%28x%29sin%28pi%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the given identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2Bpi%2F2%29+=+cos%28x%29%2A%280%29-sin%28x%29%281%29 ALIGN=MIDDLE  ALT=\"cos%28x%2Bpi%2F2%29+=+cos%28x%29%2A%280%29-sin%28x%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the unit circle\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2Bpi%2F2%29+=+0-sin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%2Bpi%2F2%29+=+0-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2Bpi%2F2%29+=+-sin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%2Bpi%2F2%29+=+-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. We'll call this Equation C\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F2-x%29+=+cos%28pi%2F2%29%2Acos%28x%29%2Bsin%28pi%2F2%29sin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F2-x%29+=+cos%28pi%2F2%29%2Acos%28x%29%2Bsin%28pi%2F2%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the given identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F2-x%29+=+0%2Acos%28x%29%2B1%2Asin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F2-x%29+=+0%2Acos%28x%29%2B1%2Asin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the unit circle\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F2-x%29+=+0%2Bsin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F2-x%29+=+0%2Bsin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F2-x%29+=+sin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F2-x%29+=+sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. We'll call this Equation D\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28pi%2F2-x%29+=+1%2F%28cos%28pi%2F2-x%29%29 ALIGN=MIDDLE  ALT=\"sec%28pi%2F2-x%29+=+1%2F%28cos%28pi%2F2-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the identity sec = 1/cos.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28pi%2F2-x%29+=+1%2F%28sin%28x%29%29 ALIGN=MIDDLE  ALT=\"sec%28pi%2F2-x%29+=+1%2F%28sin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute (see Equation D). We'll call this Equation E\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%2Bpi%2F2%29=%28sin%28x%2Bpi%2F2%29%29%2F%28cos%28x%2Bpi%2F2%29%29 ALIGN=MIDDLE  ALT=\"tan%28x%2Bpi%2F2%29=%28sin%28x%2Bpi%2F2%29%29%2F%28cos%28x%2Bpi%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the identity tan = sin/cos\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%2Bpi%2F2%29=%28cos%28x%29%29%2F%28cos%28x%2Bpi%2F2%29%29 ALIGN=MIDDLE  ALT=\"tan%28x%2Bpi%2F2%29=%28cos%28x%29%29%2F%28cos%28x%2Bpi%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Perform a substitution (see equation B)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%2Bpi%2F2%29=%28cos%28x%29%29%2F%28-sin%28x%29%29 ALIGN=MIDDLE  ALT=\"tan%28x%2Bpi%2F2%29=%28cos%28x%29%29%2F%28-sin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Perform a substitution (see equation C)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%2Bpi%2F2%29=-%28cos%28x%29%29%2F%28sin%28x%29%29 ALIGN=MIDDLE  ALT=\"tan%28x%2Bpi%2F2%29=-%28cos%28x%29%29%2F%28sin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. We'll call this Equation F\r<BR>\n" );
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document.write( "Now onto the main problem\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sin%28x%29%2Atan%28x%2Bpi%2F2%29%2Asec%28pi%2F2-x%29 ALIGN=MIDDLE  ALT=\"-sin%28x%29%2Atan%28x%2Bpi%2F2%29%2Asec%28pi%2F2-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply a substitution (see equation A)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sin%28x%29%2A%28-%28cos%28x%29%29%2F%28sin%28x%29%29%29%2Asec%28pi%2F2-x%29 ALIGN=MIDDLE  ALT=\"-sin%28x%29%2A%28-%28cos%28x%29%29%2F%28sin%28x%29%29%29%2Asec%28pi%2F2-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply a substitution (see equation F)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sin%28x%29%2A%28-%28cos%28x%29%29%2F%28sin%28x%29%29%29%2A%281%2F%28sin%28x%29%29%29 ALIGN=MIDDLE  ALT=\"-sin%28x%29%2A%28-%28cos%28x%29%29%2F%28sin%28x%29%29%29%2A%281%2F%28sin%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply a substitution (see equation E)\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%29%2Atan%28x%2Bpi%2F2%29%2Asec%28pi%2F2-x%29 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%29%2Atan%28x%2Bpi%2F2%29%2Asec%28pi%2F2-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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