document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206148>Question 1206148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you simplify the following equation with trigonometry identities?\r<BR>\n" );
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document.write( "tanθ/1-cos^2θ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843398 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=843398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%28theta%29%29%2F%281+-+cos%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"%28tan%28theta%29%29%2F%281+-+cos%5E2%28theta%29%29\"   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=%28tan%28theta%29%29%2F%28sin%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"%28tan%28theta%29%29%2F%28sin%5E2%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the pythagorean trig identity\r<BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2Ctan%28theta%29%2C%22divide%22%2Csin%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C3%2Ctan%28theta%29%2C%22divide%22%2Csin%5E2%28theta%29%29\"   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=matrix%281%2C3%2Csin%28theta%29%2Fcos%28theta%29%2C%22divide%22%2Csin%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C3%2Csin%28theta%29%2Fcos%28theta%29%2C%22divide%22%2Csin%5E2%28theta%29%29\"   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=%28sin%28theta%29%2Fcos%28theta%29%29%2A%281%2F%28sin%5E2%28theta%29%29%29 ALIGN=MIDDLE  ALT=\"%28sin%28theta%29%2Fcos%28theta%29%29%2A%281%2F%28sin%5E2%28theta%29%29%29\"   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=%281%2Fcos%28theta%29%29%2A%281%2Fsin%28theta%29%29 ALIGN=MIDDLE  ALT=\"%281%2Fcos%28theta%29%29%2A%281%2Fsin%28theta%29%29\"   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=sec%28theta%29%2Acsc%28theta%29 ALIGN=MIDDLE  ALT=\"sec%28theta%29%2Acsc%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%28theta%29%29%2F%281+-+cos%5E2%28theta%29%29+=+sec%28theta%29%2Acsc%28theta%29 ALIGN=MIDDLE  ALT=\"%28tan%28theta%29%29%2F%281+-+cos%5E2%28theta%29%29+=+sec%28theta%29%2Acsc%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is an identity.\r<BR>\n" );
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document.write( "Alternatively,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fcos%28theta%29%29%2A%281%2Fsin%28theta%29%29 ALIGN=MIDDLE  ALT=\"%281%2Fcos%28theta%29%29%2A%281%2Fsin%28theta%29%29\"   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=1%2F%28cos%28theta%29%2Asin%28theta%29%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28cos%28theta%29%2Asin%28theta%29%29%29\"   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=1%2F%280.5sin%282theta%29%29%29 ALIGN=MIDDLE  ALT=\"1%2F%280.5sin%282theta%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use a variation of sin(2theta) = 2*sin(theta)*cos(theta)\r<BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28sin%282theta%29%29 ALIGN=MIDDLE  ALT=\"2%2F%28sin%282theta%29%29\"   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=2csc%282theta%29 ALIGN=MIDDLE  ALT=\"2csc%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we could also say that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%28theta%29%29%2F%281+-+cos%5E2%28theta%29%29+=+2csc%282theta%29 ALIGN=MIDDLE  ALT=\"%28tan%28theta%29%29%2F%281+-+cos%5E2%28theta%29%29+=+2csc%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is an identity.\r<BR>\n" );
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document.write( "You can use a graphing calculator to verify each identity. <BR>\n" );
document.write( "Desmos is one good choice.<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.desmos.com/calculator/jwy2tauhgg\">https://www.desmos.com/calculator/jwy2tauhgg</a><BR>\n" );
document.write( "Notice how one curve overlaps the other perfectly. Click each curve on/off to help show the overlap (the curve should blink different colors).<BR>\n" );
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