document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=852861>Question 852861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression\r<BR>\n" );
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document.write( "sin^2x + sin^2 x cot^2 x\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "sin^2x-1/cos(-x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #513719 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=513719\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given;<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2B+sin%5E2%28x%29%2Acot%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2B+sin%5E2%28x%29%2Acot%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the identity<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%29+=+cos%28x%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%29+=+cos%28x%29%2Fsin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and square both sides to get<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%5E2%28x%29+=+cos%5E2%28x%29%2Fsin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"cot%5E2%28x%29+=+cos%5E2%28x%29%2Fsin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute (3) into (1) and get<BR>\n" );
document.write( "(4)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2B+sin%5E2%28x%29%2Acos%5E2%28x%29%2Fsin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2B+sin%5E2%28x%29%2Acos%5E2%28x%29%2Fsin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "(5)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2B+cos%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2B+cos%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since<BR>\n" );
document.write( "(6) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You have<BR>\n" );
document.write( "(7)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2B+sin%5E2%28x%29%2Acot%5E2%28x%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2B+sin%5E2%28x%29%2Acot%5E2%28x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Answer: 1<BR>\n" );
document.write( "Also given<BR>\n" );
document.write( "(8) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%5E2%28x%29+-+1%29%2Fcos%28-x%29 ALIGN=MIDDLE  ALT=\"%28sin%5E2%28x%29+-+1%29%2Fcos%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using (6) we get<BR>\n" );
document.write( "(9) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+=+1+-+cos%5E2%28x%29+ ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+=+1+-+cos%5E2%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now put (9) into (8) to get<BR>\n" );
document.write( "(10) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+1+-+cos%5E2%28x%29+-+1%29%2Fcos%28-x%29 ALIGN=MIDDLE  ALT=\"%28+1+-+cos%5E2%28x%29+-+1%29%2Fcos%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "(11)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-cos%5E2%28x%29%29%2Fcos%28-x%29 ALIGN=MIDDLE  ALT=\"%28-cos%5E2%28x%29%29%2Fcos%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <BR>\n" );
document.write( "Since the cosine is an even function we have<BR>\n" );
document.write( "(12) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28-x%29+=+cos%28x%29 ALIGN=MIDDLE  ALT=\"+cos%28-x%29+=+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then (11) reduces to<BR>\n" );
document.write( "(13) <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;\" ><BR>\n" );
document.write( "Answer: <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;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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