document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628525>Question 628525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> need help proving (2tan(alpha))/(1+tan^2(alpha))=sin(2)alpha\r<BR>\n" );
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document.write( "and also this one tan(B-a) if sin(a)alpha=4/5 and cos(B) beta= -12/13 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395720 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=395720\">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=%282tan%28alpha%29%29%2F%281%2Btan%5E2%28alpha%29%29=sin%282%2Aalpha%29 ALIGN=MIDDLE  ALT=\"%282tan%28alpha%29%29%2F%281%2Btan%5E2%28alpha%29%29=sin%282%2Aalpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When you don't see any better solutions, it is a good idea to rewrite any tan's, cot's, sec's and csc's in terms of sin and/or cos. Since I do not yet see a faster solution, this is what I will do:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28sin%28alpha%29%2Fcos%28alpha%29%29%29%2F%281%2B%28sin%28alpha%29%2Fcos%28alpha%29%29%5E2%29=sin%282%2Aalpha%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "TO get rid of the fractions within the fraction, we multiply the numerator and denominator of the \"big\" fraction by the least common denominator (LCD) of all the \"little\" fractions. THe LCD here is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28alpha%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28cos%28alpha%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%28sin%28alpha%29%2Fcos%28alpha%29%29%29%2F%281%2B%28sin%28alpha%29%2Fcos%28alpha%29%29%5E2%29%29%28%28cos%28alpha%29%29%5E2%2F%28cos%28alpha%29%29%5E2%29=sin%282%2Aalpha%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the numerator, one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28alpha%29+ ALIGN=MIDDLE  ALT=\"cos%28alpha%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cancels. In the denominator we use the Distributive property:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282sin%28alpha%29cos%28alpha%29%29%2F%28%28cos%28alpha%29%29%5E2+%2B+%28sin%28alpha%29%29%5E2%29+=+sin%282%2Aalpha%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We should now recognize both the numerator and denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282%2Aalpha%29%2F1+=+sin%282%2Aalpha%29 ALIGN=MIDDLE  ALT=\"sin%282%2Aalpha%29%2F1+=+sin%282%2Aalpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282%2Aalpha%29+=+sin%282%2Aalpha%29 ALIGN=MIDDLE  ALT=\"sin%282%2Aalpha%29+=+sin%282%2Aalpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And we are finished!<br><BR>\n" );
document.write( "The second problem is impossible to solve without knowing what quadrants alpha and beta terminate in. </SPAN>\n" );
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