document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109301>Question 109301</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0136150624/algebrahomeworkh>Algebra and Trigonomometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Prove that Sin(theta)times Cos(theta) divided by Cos^2(theta)-Sin^2(theta)=Tan(theta) divided by 1-Tan(theta)<BR>\n" );
document.write( "Show step by step how to change the left to equal the right side of equasion<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79695 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=79695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm going to use the double angle identities <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin(2\theta)=2\sin(\theta)\cos(\theta)\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \cos(2\theta)=\cos^{2}(\theta)-\sin^{2}(\theta)\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \tan(2\theta)=\frac{2\tan(\theta)}{1-\tan(\theta)}\">\r<BR>\n" );
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document.write( "Notice how we have <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos(\theta)\sin(\theta)\"> in the problem. So we must divide both sides of the identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin(2\theta)=2\sin(\theta)\cos(\theta)\"> by 2 to get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{2}\sin(2\theta)=\sin(\theta)\cos(\theta)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \begin{align*} \frac{\cos(\theta)\sin(\theta)}{\cos^{2}(\theta)-\sin^{2}(\theta)}&=\frac{\tan(\theta)}{1-\tan(\theta)} \\ \frac{\frac{1}{2}\sin(2\theta)}{\cos^{2}(\theta)-\sin^{2}(\theta)}&= \mbox{ Use the first identity listed}\\ \frac{\frac{1}{2}\sin(2\theta)}{\cos(2\theta)}&=\mbox{ Use the second identity listed}\\ \frac{1}{2}\tan(2\theta)&= \mbox{ Replace sine over cosine with tangent}\\ \frac{1}{2}\frac{2\tan(\theta)}{1-\tan(\theta)}&= \mbox{ Use the third identity listed}\\ \frac{\tan(\theta)}{1-\tan(\theta)}&= \mbox{ Simplify}\\ \end{align*}\"> </SPAN>\n" );
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