document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=675437>Question 675437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Verify that each equation is an identity.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28alpha-beta%29%2Fcos%28alpha%29sin%28beta%29 ALIGN=MIDDLE  ALT=\"cos%28alpha-beta%29%2Fcos%28alpha%29sin%28beta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = tan(alpha)+cot(beta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #419843 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=419843\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28alpha-beta%29%2Fcos%28alpha%29sin%28beta%29+=+tan%28alpha%29%2Bcot%28beta%29 ALIGN=MIDDLE  ALT=\"cos%28alpha-beta%29%2Fcos%28alpha%29sin%28beta%29+=+tan%28alpha%29%2Bcot%28beta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the arguments on the right side are just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta ALIGN=MIDDLE  ALT=\"beta\"   DISABLED_style= \"max-width:90%; height:auto;\" >, I'm going to use the cos(A-B) formula on the numerator of the left side so that all the arguments are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta ALIGN=MIDDLE  ALT=\"beta\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28alpha%29cos%28beta%29+%2B+sin%28alpha%29sin%28beta%29%29%2Fcos%28alpha%29sin%28beta%29+=+tan%28alpha%29%2Bcot%28beta%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since the right side has two terms I'm going to split the fraction on the left into two terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28alpha%29cos%28beta%29%2Fcos%28alpha%29sin%28beta%29+%2B+sin%28alpha%29sin%28beta%29%2Fcos%28alpha%29sin%28beta%29++=+tan%28alpha%29%2Bcot%28beta%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Each of the new fractions will reduce:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28beta%29%2Fsin%28beta%29+%2B+sin%28alpha%29%2Fcos%28alpha%29+=+tan%28alpha%29%2Bcot%28beta%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The first fraction is cot and the second is tan:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28beta%29+%2B+tan%28alpha%29+=+tan%28alpha%29%2Bcot%28beta%29 ALIGN=MIDDLE  ALT=\"cot%28beta%29+%2B+tan%28alpha%29+=+tan%28alpha%29%2Bcot%28beta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since addition is commutative we can change the order:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28alpha%29+%2B+cot%28beta%29+=+tan%28alpha%29%2Bcot%28beta%29 ALIGN=MIDDLE  ALT=\"tan%28alpha%29+%2B+cot%28beta%29+=+tan%28alpha%29%2Bcot%28beta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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