document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130978>Question 130978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to prove that tan^2(x) - sin^(x) = tan^(x) sin^2(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95613 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=95613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's manipulate the left side to transform it into the right side (note: we are not going to even touch the right side)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan^2\left(x\right)-\sin^2\left(x\right)\">  .... Start with the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE =\frac{\sin^2\left(x\right)}{\cos^2\left(x\right)}-\sin^2\left(x\right)\">  .... Rewrite <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \tan^2\left(x\right)\"> as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{\sin^2\left(x\right)}{\cos^2\left(x\right)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE =\frac{\sin^2\left(x\right)}{\cos^2\left(x\right)}-\sin^2\left(x\right)\left(\frac{\cos^2\left(x\right)}{\cos^2\left(x\right)\right)\">   .... Multiply <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin^2\left(x\right)\"> by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{\cos^2\left(x\right)}{\cos^2\left(x\right)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE =\frac{\sin^2\left(x\right)}{\cos^2\left(x\right)}-\frac{\sin^2\left(x\right)\cos^2\left(x\right)}{\cos^2\left(x\right)}\">   .... Multiply \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE =\frac{\sin^2\left(x\right)-\sin^2\left(x\right)\cos^2\left(x\right)}{\cos^2\left(x\right)}\">   .... Combine the fractions. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE =\frac{\sin^2\left(x\right)\left(1-\cos^2\left(x\right)\right)}{\cos^2\left(x\right)}\">   .... Factor out <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin^2\left(x\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE =\frac{\sin^2\left(x\right)\left(sin^2\left(x\right)\right)}{\cos^2\left(x\right)}\">   .... Replace <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1-\cos^2\left(x\right)\"> with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin^2\left(x\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE =\tan^2\left(x\right)\sin^2\left(x\right)\">   .... Replace <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{\sin^2\left(x\right)}{\cos^2\left(x\right)}\">  with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \tan^2\left(x\right)\">\r<BR>\n" );
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document.write( "So this shows us that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan^2\left(x\right)-\sin^2\left(x\right)=\tan^2\left(x\right)\sin^2\left(x\right)\">      </SPAN>\n" );
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