document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157780>Question 1157780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Eliminate θ, if<BR>\n" );
document.write( "x = 3cosecθ + 4cotθ<BR>\n" );
document.write( "y = 4cosecθ - 3cotθ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780720 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20063)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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/cgi-bin/show-face.mpl?user=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780720\">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=system%28x+=+3csc%28theta%29+%2B+4cot%28theta%29%2C%0D%0Ay+=+4csc%28theta%29+-+3cot%28theta%29%29 ALIGN=MIDDLE   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=system%283csc%28theta%29+%2B+4cot%28theta%29=x%2C%0D%0A4csc%28theta%29+-+3cot%28theta%29=y%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use Cramer's rule (or substitution or addition, but Cramer's rule is easiest) <BR>\n" );
document.write( "to solve for csc(θ) and cot(θ)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C9%2C%0D%0Acsc%28theta%29%2C%22%22=%22%22%2Cabs%28matrix%282%2C2%2Cx%2C4%2Cy%2C-3%29%29%2Fabs%28matrix%282%2C2%2C3%2C4%2C4%2C-3%29%29%2C%0D%0A%22%22=%22%22%2C%28-3x-4y%29%2F%28-9-16%29%2C%22%22=%22%22%2C%283x%2B4y%29%2F%289%2B16%29%2C%22%22=%22%22%2C%283x%2B4y%29%2F25%2C%0D%0A%22%22%2C%22%22%2C%22%22%2C%22%22%2C%22%22%2C%22%22%2C%22%22%2C%22%22%2C%22%22%2C%0D%0Acot%28theta%29%2C%22%22=%22%22%2Cabs%28matrix%282%2C2%2C3%2Cx%2C4%2Cy%29%29%2Fabs%28matrix%282%2C2%2C3%2C4%2C4%2C-3%29%29%2C%0D%0A%22%22=%22%22%2C%283y-4x%29%2F%28-9-16%29%2C%22%22=%22%22%2C%283y-4x%29%2F%289%2B16%29%2C%22%22=%22%22%2C%283y%2B4x%29%2F25%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next we use the identity \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C3%2C%0D%0A%0D%0A1%2Bcot%5E2%28theta%29%2C%22%22=%22%22%2Ccsc%5E2%28theta%29%2C%0D%0A%0D%0A%0D%0A1%2B%28%283y%2B4x%29%2F25%29%5E2%2C%22%22=%22%22%2C%28%283x%2B4y%29%2F25%29%5E2%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can simplify that and get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2+-+7y%5E2+%2B+625+=+0 ALIGN=MIDDLE  ALT=\"7x%5E2+-+7y%5E2+%2B+625+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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