document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196469>Question 1196469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that x = sec^2θ and y+2 = cot^2θ, find y in terms of x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829306 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829306\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sec%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"x+=+sec%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx+=+1%2F%28sec%5E2%28theta%29%29+=+cos%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"1%2Fx+=+1%2F%28sec%5E2%28theta%29%29+=+cos%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check out this list of trig identities<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf\">https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf</a><BR>\n" );
document.write( "Look under the \"pythagorean identities\" subsection, on page 2, to find the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+cot%5E2%28theta%29+=+csc%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"1+%2B+cot%5E2%28theta%29+=+csc%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This rearranges to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%5E2%28theta%29+=+csc%5E2%28theta%29-1 ALIGN=MIDDLE  ALT=\"cot%5E2%28theta%29+=+csc%5E2%28theta%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we could say:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2+=+cot%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"y%2B2+=+cot%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2+=+csc%5E2%28theta%29-1 ALIGN=MIDDLE  ALT=\"y%2B2+=+csc%5E2%28theta%29-1\"   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=y+=+csc%5E2%28theta%29-1-2 ALIGN=MIDDLE  ALT=\"y+=+csc%5E2%28theta%29-1-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+csc%5E2%28theta%29-3 ALIGN=MIDDLE  ALT=\"y+=+csc%5E2%28theta%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1%2F%28sin%5E2%28theta%29%29-3 ALIGN=MIDDLE  ALT=\"y+=+1%2F%28sin%5E2%28theta%29%29-3\"   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=y+=+1%2F%281-cos%5E2%28theta%29%29-3 ALIGN=MIDDLE  ALT=\"y+=+1%2F%281-cos%5E2%28theta%29%29-3\"   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=y+=+1%2F%281-1%2Fx%29-3 ALIGN=MIDDLE  ALT=\"y+=+1%2F%281-1%2Fx%29-3\"   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=y+=+1%2F%28x%2Fx-1%2Fx%29-3 ALIGN=MIDDLE  ALT=\"y+=+1%2F%28x%2Fx-1%2Fx%29-3\"   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=y+=+1%2F%28%28x-1%29%2Fx%29-3 ALIGN=MIDDLE  ALT=\"y+=+1%2F%28%28x-1%29%2Fx%29-3\"   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=y+=+x%2F%28x-1%29+-+3 ALIGN=MIDDLE  ALT=\"y+=+x%2F%28x-1%29+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We could optionally continue like so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%2F%28x-1%29+-+3 ALIGN=MIDDLE  ALT=\"y+=+x%2F%28x-1%29+-+3\"   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=y+=+x%2F%28x-1%29+-+3%28x-1%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"y+=+x%2F%28x-1%29+-+3%28x-1%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x+-+3%28x-1%29%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"y+=+%28x+-+3%28x-1%29%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x+-+3x%2B3%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"y+=+%28x+-+3x%2B3%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2x%2B3%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"y+=+%28-2x%2B3%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );