document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95717>Question 95717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sorry. Last one was screwed up.\r<BR>\n" );
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document.write( "sinx/sinx+cosx = tanx/1+tanx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69744 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=69744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinx%2F%28sinx%2Bcosx%29+=+tanx%2F%281%2Btanx%29 ALIGN=MIDDLE  ALT=\"sinx%2F%28sinx%2Bcosx%29+=+tanx%2F%281%2Btanx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use the identity:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tanx+=+sinx%2Fcosx ALIGN=MIDDLE  ALT=\"tanx+=+sinx%2Fcosx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and on the right side substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinx%2Fcosx ALIGN=MIDDLE  ALT=\"sinx%2Fcosx\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tanx ALIGN=MIDDLE  ALT=\"tanx\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2F%281%2B%28sinx%2Fcosx%29%29 ALIGN=MIDDLE  ALT=\"sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2F%281%2B%28sinx%2Fcosx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The denominator contains 1. Replace 1 with an equivalent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cosx%2Fcosx ALIGN=MIDDLE  ALT=\"cosx%2Fcosx\"   DISABLED_style= \"max-width:90%; height:auto;\" > to make the equation<BR>\n" );
document.write( "become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2F%28%28cosx%2Fcosx%29%2B%28sinx%2Fcosx%29%29 ALIGN=MIDDLE  ALT=\"sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2F%28%28cosx%2Fcosx%29%2B%28sinx%2Fcosx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice now that the two terms in the denominator both have the common denominator <BR>\n" );
document.write( "of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cosx ALIGN=MIDDLE  ALT=\"cosx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Because they have the common denominator their numerators can be added over <BR>\n" );
document.write( "that common denominator to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2F%28%28cosx%2Bsinx%29%2Fcosx%29 ALIGN=MIDDLE  ALT=\"sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2F%28%28cosx%2Bsinx%29%2Fcosx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that on the right side you are dividing by the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28cosx%2Bsinx%29%2Fcosx%29 ALIGN=MIDDLE  ALT=\"%28%28cosx%2Bsinx%29%2Fcosx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To divide by a fraction you can invert the fraction and multiply. This converts the problem<BR>\n" );
document.write( "to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2A%28%28cosx%29%2F%28cosx%2Bsinx%29%29 ALIGN=MIDDLE  ALT=\"sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2A%28%28cosx%29%2F%28cosx%2Bsinx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the right side cancel the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cosx ALIGN=MIDDLE  ALT=\"cosx\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms in the denominator and numerator:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinx%2F%28sinx%2Bcosx%29+=+%28%28sinx%29%2F%28cross%28cosx%29%29%29%2A%28%28cross%28cosx%29%29%2F%28cosx%2Bsinx%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that with this set of cancellations the right side now equals the left side of<BR>\n" );
document.write( "the equation. Therefore, the original problem has been proven.<BR>\n" );
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document.write( "Hope this helps you to understand trig a little better.<BR>\n" );
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