document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=307241>Question 307241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is proving a trigonometric equation.\r<BR>\n" );
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document.write( "Verify cos(x))/(1-sin(x))=sec(x)+tan(x)\r<BR>\n" );
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document.write( "All I can figure out is how to expand it somewhat to be <BR>\n" );
document.write( "cos(x)/(1-sin(x)=(1/cos(x))+(sin(x)/cos(x)   I have no clue where to go now.\r<BR>\n" );
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document.write( "Please help.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #219831 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=219831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\cos(x)}{1-\sin(x)} = \sec(x)+\tan(x)\"> ... Start with the given equation.\r<BR>\n" );
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document.write( "We're only going to manipulate the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\cos(x)(1+\sin(x))}{(1-\sin(x))(1+\sin(x))} = \sec(x)+\tan(x)\"> ... Multiply both numerator and denominator of the left side by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 1+\sin(x)\"> \r<BR>\n" );
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document.write( "Think of of the last step as rationalizing the denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\cos(x)(1+\sin(x))}{1-\sin^2(x)} = \sec(x)+\tan(x)\"> ... FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\cos(x)+\cos(x)\sin(x)}{1-\sin^2(x)} = \sec(x)+\tan(x)\"> ... Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\cos(x)+\cos(x)\sin(x)}{\cos^2(x)} = \sec(x)+\tan(x)\"> ... Replace <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 1-\sin^2(x)\"> with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos^2(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\cos(x)}{\cos^2(x)}+\frac{\cos(x)\sin(x)}{\cos^2(x)} = \sec(x)+\tan(x)\"> ... Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{\cos(x)}+\frac{\sin(x)}{\cos(x)} = \sec(x)+\tan(x)\"> ... Cancel out like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sec(x)+\tan(x) = \sec(x)+\tan(x)\"> ... Use the identities <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{\cos(x)}=\sec(x)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\sin(x)}{\cos(x)}=\tan(x)\">\r<BR>\n" );
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document.write( "Since the two sides are identical, this verifies the identity. </SPAN>\n" );
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